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PH3-MI (Medical Imaging)
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Course Lecturer: David Bradley
Office 18BC04. Extension 3771
E-mail: [email protected]
Content: an introduction to imaging using
ionising radiations, focusing on CT; use of
non-ionising radiations, focusing on
ultrasound imaging and MRI.
Medical imaging using ionising
radiations
• Medical imaging has come a long way
since 1895 when Röntgen first
described a ‘new kind of ray’.
• That X-rays could be used to display
anatomical features on a photographic
plate was of immediate interest to the
medical community at the time.
• Today a scan can refer to any one of a
number of medical-imaging techniques
used for diagnosis and treatment.
Digital Systems
• The transmission and detection of X-rays still lies
at the heart of radiography, angiography,
fluoroscopy and conventional mammography
examinations.
• However, traditional film-based scanners are
gradually being replaced by digital systems
• The end result is the data can be viewed, moved
and stored without a single piece of film ever
being exposed.
Detail detectability; test
phantoms
Detail-detectability
The Physical Probe
• X-rays also form basis of computed tomography (CT)
systems, which can obtain a series of 2D "slices"
through body.
• Other physical techniques also used: single photon
emission CT (SPECT) and positron emission
tomography (PET) rely on use and properties of
radionuclides,while MRI exploits well known
principles of NMR, and is starting point for fMRI.
• Last but not least, ultrasound uses high-frequency
sound in similar manner to submarine sonar to
produce images of tissue and blood vessels.
Prospects
• Even if patients remain absolutely still while being
scanned, a beating heart or the movements
associated with breathing can sometimes distort
the final images.
• We therefore look forward to "intelligent
acquisition" systems that allow for the effects of
patient motion.
Live-time imaging: fluoroscopy
• Used for obtaining cine x-ray images of a patient
in functional studies.
• Radiologist uses switch to limit x-ray beam
transmitted through patient. Transmitted beam
falls upon fluorescent screen coupled to an ‘image
intensifier’ coupled to a TV camera.
• Fluoroscopy often used to observe digestive tract.
Also used during diagnostic and therapeutic
procedures, observing action of instrument used to
diagnose or treat patient.
X-ray Image Intensifiers (II)
for Fluoroscopy
• X-ray II converts transmitted x rays into
brightened, visible light image.
• Within II, input phosphor converts the x-ray
photons to light photons, which are then converted
to photoelectrons within photocathode.
• The electrons are accelerated and focused by series
of electrodes striking output phosphor, which
converts accelerated electrons into light photons
that may be captured by various imaging devices.
Image Intensifier
• Through this process, several thousand light
photons are produced for each x-ray photon
reaching the input phosphor.
• Most modern image intensifiers use CsI2 for input
phosphor because it has high absorption efficiency
and thus decreases patient dose.
• Image intensifiers come in various sizes, most
having more than one input image size or
magnification mode.
Magnification Modes and Spatial
Resolution
• Changing voltage to electronic lenses of II will change
magnification of II.
• In magnification, smaller area of the input phosphor is
used, giving effect of zooming.
• Because input field size is reduced, exposure to input
phosphor must be increased to maintain constant
brightness level at output phosphor.
• To maintain same noise level, dose quadruples when
magnification doubled.
• The smaller the field size, the larger the magnification
& the higher the patient dose.
• Higher magnification modes produce increased spatial
resolution. Spatial resolution of II in range 4–6 lp/mm.
Spatial resolution of system depends on other imaging
components in imaging chain.
Fate of a 50 keV x-ray photon totally
absorbed in input phosphor
• Absorption will result in ~ 2 x 103 light photons. Half of
these might reach photocathode.
• If efficiency of photocathode 15%, ~ 150 electrons
released.
• If acceleration voltage 25 kV, efficiency of electron optics
is 90% and each 25 keV electron releases 2 x 103 light
photons in output phosphor, then ~ 2.7 x 105 light photons
produced.
• If 70% of these transmitted through output window,
outcome is light pulse of ~ 2 x 105 photons produced
following absorption of a single 50 keV x-ray.
Performance Characteristics
• Brightness Gain The gain in image brightness
results from combined effects of image minification
and acceleration of the electrons:
• Minification Gain Obtained because electrons from
relatively large photocathode focused down to
smaller area of output phosphor. Gives rise to an
increase in number of electrons/mm2. Gain is given
by ratio of areas of input and output phosphors,
expressed as:
( Diameter of Input Phosphor ) 2
Minificati on Gain 
( Diameter of Output Phosphor ) 2
• Thus, for input phosphors with diameters between 15
and 40 cm and output phosphor of 2.5 cm diameter,
minification gain is between 36 and 256.
• Flux Gain Results from acceleration given to
electrons as they are attracted from photocathode to
output phosphor. Dependent on applied voltage and
typically between 50 and 100.
• Brightness Gain Overall brightness gain given by:
Brightness Gain = (Minification Gain) x (Flux Gain)
• Thus, when: Minification Gain = 100 and Flux Gain
= 50 then Brightness Gain = 5,000. Brightness Gains
to more than 10,000 are achievable
Limiting Spatial Resolution
• This can be assessed using a Pb bar test pattern,
determining highest spatial frequency that can be
resolved and given in line pairs per mm (lp/mm).
• Images of a test pattern are shown in figure
below, where a 23 cm II is operated in 23 cm
(left), 15 cm (middle) and 11 cm (right) mode. The
parameter is generally expressed for centre of field
of view, since it decreases towards image
periphery depending on quality of electron optics.
Field Size
(cm)
Output
Phosphor
100/105
mm
Camera
15 - 18
5 lp/mm
4.2 lp/mm
2.5 lp/mm
23 - 25
4.2 lp/mm
3.7 lp/mm
2.2 lp/mm
35 mm
Camera
Conventio
nal Video
System
1.5 - 1.3
lp/mm
1.0 - 0.9
lp/mm
• Resolution
General Principles
Ability to discern two points close together
Unresolved
Resolved
• Contrast
General Principles
Ability to discern interesting object from noise or other tissues
Poor Contrast
Good Contrast
CT scanning and reconstruction
• As in MRI, computed tomography is a method that
can be used to create cross-sectional images.
• CT refers to a generalised methodology for image
reconstruction, the practical techniques of which can
be sub-divided into attenuation CT and emission CT.
• Examples of latter include PET and SPECT. In this
course, we will consider attenuation CT and, in
particular, x-ray CT.
CT imaging
• Goal of x-ray CT is to reconstruct an image whose
signal intensity at every point in region imaged is
proportional to μ (x, y, z), where μ is linear
attenuation coefficient for x-rays.
• In practice, μ is a function of x-ray energy as well
as position and this introduces a number of
complications that we will not investigate here.
• X-ray CT is now a mature (though still rapidly
developing) technology and a vital component of
hospital diagnosis.
Principles of x-ray attenuation
• Attenuation CT imaging based on Beer’s Law,
describing how an x-ray beam is reduced in intensity
as it passes through a medium.
• In a uniform substance of linear attenuation
coefficient μ, x-ray “intensity”, as measured by a
detector placed at depth d is
I (d )  I 0 exp(  d )
where I0 is intensity measured at depth zero.
[1]
• Suppose we now consider a set of blocks of different
material, each of width Δy. The x-ray intensity
measured at the exit of the set of blocks is
I (ny)  I 0 exp( 1y)  exp( 2 y)  exp( 3y)
 n

[2]
 I 0 exp   i y 
 i 1

• For the limit Δy  0, N  , this becomes




I  I 0 exp   μ( y )dy 
 across

sample


[3]
Fig 1: Schematic diagram of a 1st
generation CT scanner
(a)
(b)
X-ray detector
y
x
“Real” space
coordinate
system (x, y)
y
x
Rotated coordinate
system (x, y)
X-ray source

Source and detector slide
in tandem on gantry
(a) X-ray source projects a thin “pencil” beam of x-rays through
sample, detected on the other side of the sample. Source and detector
move in tandem along a gantry. (b) Whole gantry rotates, allowing
projection data to be acquired at different angles.
First-generation CT apparatus
• As shown in Fig 1a, the first-generation CT apparatus
consisted of a source and detector, placed on either
side of object to be imaged. These slide along in
tandem.
• Consider intensity of x-ray signal received by detector
when source-detector assembly is at position x :

I ( x)  I 0 exp    ( x, y )dy

[4]
EMI CT head scanner (Mayo Clinic, Rochester, Minn, circa 1973)
and an 80 x 80-matrix head CT image obtained with it.
General Principles
• Image Display - Pixels and voxels
The Radon transformation
• In a first-generation scanner, the source-detector track
can rotate around the sample, as shown in Fig 1. We
will denote the “x-axis” along which the assembly
slides when the assembly is at angle φ by xφ and the
perpendicular axis by yφ.
• Clearly, we may relate our (xφ, yφ) coordinates to the
coordinates in the un-rotated lab frame by
xr  x cos   y sin 
yr   x sin   y cos 
[5]
Figure 2: Relationship between
Real Space and Radon Space
Real (Image) Space
y
Radon Space
Convert I(x) to (x)
y

Store the result (x) at the
point (x ) in Radon space
x

x
Typical path of X-rays
through sample, leading to
detected intensity I(x)
Highlighted point on right shows where the value λφ (xφ) created by passing
the x-ray beam through the sample at angle φ and point xφ is placed. Note
that, as is conventional, the range of φ is [-π / 2, +π / 2], since the remaining
values of φ simply duplicate this range in the ideal case.
x
• Hence, the “projection signal” when the gantry is
at angle φ is
[6]
I ( x )  I exp   ( x , y )dy


0





• We define the Radon transform as
 I ( x ) 

 ( x )    ( x , y )dy   ln 
 I0 
sample
[7]
Radon Space
• We define a new “space”, called Radon space, in
much the same way as one defines reciprocal
domains in a 2-D Fourier transform. Radon space
has two dimensions xφ and φ . At the general point
(xφ, φ), we “store” the result of the projection
λφ(xφ).
• Taking lots of projections at a complete range of
xφ and φ “fills” Radon space with data, in much
the same way that we filled Fourier space with our
2-D MRI data.
Fig 3. Sinograms for sample consisting of a
small number of isolated objects.
Real (Image) Space
Radon Space


y
x
x
Single point
(x0, y0)
Corresponding
sinogram track

In this diagram, the full range of φ is [-π, +π ] is displayed.
Relationship between “real
space” and Radon space
• Consider how the sinogram for a sample
consisting of a single point in real (image) space
will manifest in Radon space.
• For a given angle φ, all locations xφ lead to λφ(xφ)
= 0, except the one coinciding with the projection
that goes through point (x0, y0) in real space. From
Equation 5, this will be the projection where
xφ = x0 cos φ + y0 sin φ.
• Thus, all points in the Radon space corresponding to
the single-point object are zero, except along the
track
x  x0 cos   y0 sin   R cos(  0 ) [8]
where R = (x2 + y2)1/2 and φ0 = tan-1 ( y / x).
• If we have a composite object, then the filled Radon
space is simply the sum of all the individual points
making up the object (i.e. multiple sinusoids, with
different values of R and φ0). See Fig 3 for an
illustration of this.
Reconstruction of CT images
• This is performed by a process known as backprojection, for which the procedure is as follows:
• Consider one row of the sinogram, corresponding
to angle φ. Note how in Fig 3, the value of the
Radon transform λφ(xφ) is represented by the grey
level of the pixel. When we look at a single row
(i.e., a 1-D set of data), we can draw this as a
graph — see Fig 4(a). Fig 4(b) shows a typical set
of such line profiles at different projection angles.
Fig 4a. Relationship of 1-D projection
through the sample and row in
sinogram
(a)
Real (Image) Space
Radon Space


y
0
Beam path corresponds to
peak in projection, with
result stored in Radon space
x
x
Entire x-profile (i.e., set of
projections for all values of xf ) is
stored as a row in Radon space

(b)
90
Fig 4b. Projections at different
angles correspond to different rows
of the sinogram
y
x
Radon Space
45


y
x
30
x
y
x

0
y
x
Fig 4c. Back-projection of sinogram rows to form an image.
The high-intensity areas of image correspond to crossing points
of all three back-projections of profiles.
Reconstruction of CT
images (continued)
•
•
Place the sinogram row at an angle φ in
real space. Then “smear it out” evenly all
the way along the yφ -direction.
Repeat the two steps above for all the
lines in the sinogram — see Fig 4c. Where
the back-projections overlap, the signal
adds constructively to give high-intensity
image regions.
Blurring
• This is not quite the whole story. It turns out that
the image that is produced by this method is
blurred, as shown in Fig 5.
• To get exactly the right representation of the
object, we need an additional mathematical “trick”
called filtering.
Fig 5. Blurring problem with nonfiltered back-projection.
A point like object reconstructs to a blurred object. Since all objects may
be regarded as the sums of a number of point-like objects, every image will
be blurred unless the projections are first “filtered”.
General Principles- Filtered
BP
Profile
Forward
Projection
BackProjection
Object
Image
Filtered profile
Filtered
BackProjection
Filtered
Projection
Image
Further generations of CT
scanner
• The first-generation scanner described earlier is
capable of producing high-quality images.
However, since the x-ray beam must be translated
across the sample for each projection, the method
is intrinsically slow.
• Many refinements have been made over the years,
the main function of which is to dramatically
increase the speed of data acquisition.
• Scanner using different types of radiation (e.g., fan
beam) and different detection (e.g., many parallel
strips of detectors) are known as different
generations of X-ray CT scanner. We will not go
into details here but provide only an overview of
the key developments.
Four generations of CT
scanner
X-rays CT - 1st Generation
•Single X-ray Pencil Beam
(~1975)
•Single (1-D) Detector set
at 180 degrees opposed
•Simplest and cheapest
scanner type but very slow
due to
•Translate(160 steps)
•Rotate (1 degree)
•~ 5minutes (EMI CT1000)
•Higher dose than fanbeam scanners
•Scanners required head to
be surrounded by water bag
X-rays CT - 2nd
Generation (~1980)
•Narrow Fan Beam X-Ray
•Small area (2-D) detector
•Fan beam does not cover full body, so limited translation still
required
•Fan beam increases rotation step to ~10 degrees
•Faster (~20 secs/slice) and lower dose
•Stability ensured by each detector seeing non-attenuated x-ray beam
during scan
X-rays CT - 3rd
Generation (~1985)
The General Electric CTi CT scanner (1999)
[Scott & White Texas A & M University College of Medicine]
X-rays CT - 3rd
Generation
X-rays CT - 3rd
Generation
•Wide-Angle Fan-Beam X-Ray
•Large area (2-D) detector
•Rotation Only - beam covers entire scan area
•Even faster (~5 sec/slice) and even lower dose
•Need very stable detectors, as some detectors are always attenuated
•Xenon gas detectors offer best stability (and are inherently
focussed, reducing scatter)
•Solid State Detectors are more sensitive - can lead to dose
savings of up to 40% - but at the risk of ring artefacts
X-rays CT - 3rd
Generation
Spiral
•Schematic diagram of the
operation of a helical CT
scanner:
•The patient couch
translates as the x-ray
source is rotated
[http://dolphin.radiology.uiowa.edu/ge/]
X-rays CT - Multi Slice
Latest Developments Spiral, multislice CT Cardiac CT
X-rays CT - 4th
Generation (~1990)
•Wide-Angle Fan-Beam X-Ray: Rotation Only
•Complete 360 degree detector ring (Solid State - non-focussed, so
scatter is removed post-acquisition mathematically)
•Even faster (~1 sec/slice) and even lower dose
•Not widely used – difficult to stabilise rotation + expensive detector
X-rays CT - Electron Beam 4th Generation
•Fastest scanner employs electron beam, fired at ring of anode targets
around patient to generate x-rays.
•Slice acquired in ~10ms - excellent for cardiac work
CT Numbers
Linear attenuation
coefficient of each
tissue pixel is
compared with that of
water:

t   w 
CT No.  1000
w
Example values of μt:
At 80 keV:
μbone = 0.38 cm-1
μwater = 0.19 cm-1
The multiplier 1000 ensures that the CT (or
Hounsfield) numbers are whole numbers.
Windowing in CT
General Principles
• Image Display - Look up tables
Intensity
Intensity
7
7
224-255
6
6
192-223
5
5
160-191
4
4
128-159
3
3
96-127
2
2
64-95
1
1
32-63
0
0
0-31
0
128 159
255
Pixel Value
Int
Int
Pixel Value
Logarithmic
Int
Pixel Value
Exponential
Pixel Value
Inverse Linear
General Principles
• Image Display - Look up tables
Intensity
Threshold
Pixel
Value
Colour Look-up table
Window
Same image windowed to different levels
Brain image
Windowing and window level
Ring artefact in a thirdgeneration scanner
Detail-contrast diagram for a
CT scanner
Patient Dose in CT
slice thickness relative
noise    pixel size  
2
3
1
dose
or , alternatively ,
slice thickness min imum
det ectable contrast   min imum det ectable size  
2
3
1
dose
Radiation Risks
Modality
Plain x-ray
CT
MRI
Gamma camera
PET
Ultrasound
Typical Radiation
Dose (mSv)
0.02 - 5
10
2 – 20
2 - 10
-
Risk of fatal cancer - 1 in 20,000 per mSv per year
CT and corresponding
pixels in image
Simple numerical
example
The ‘decision/confusion’
matrix
Sensitivity and specificity
• The test results can be:
– True positive (TP) = A positive test result in the
presence of the disease
– True negative (TN) = A negative test result in
the absence of the disease
– False positive (FP) = A positive test result in the
absence of the disease
– False negative (FN) = A negative test result in
the presence of the disease
… sensitivity and specificity
2 x 2 table below labeled with test
result on lhs, disease status on top
Test
Positive
Test
Negative
Disease
Present
Disease
Absent
True
Positives
(TP)
False
Negatives
(FN)
False
Positive
(FP)
True
Negatives
(TN)
Sensitivity vs false-positive
rate: line D is worthless, B is
good, A is ideal
… sensitivity and
specificity
• Sensitivity: the ability of the test to identify
the disease in the presence of the disease
= TP / (TP + FN)
• Specificity: the ability of the test to exclude
the disease in the absence of the disease
= TN / (TN + FP)
Ultrasound for imaging
•
•
•
Basic principle same as used in radar and sonar
and similar to echo-location method of bats.
Emitter sends out pulses of sound. These bounce
off objects and returned echoes provide
information about object, in particular location,
size and reflectional properties.
Gases and liquids support only longitudinal
waves; solids support transverse waves as well,
but these are rapidly attenuated for non-rigid,
“soft” solids.
Basic principles
Wavefronts
Fig 1. Longitudinal waves in gas
Rarefaction
Compression
c
Reflector

Emitted pulse
Transducer
0
50
100
150
200
c
0
c
d
5 0
1 0 0
1 5 0
2 0 0
Lower amplitude
reflected pulse
• The fundamental equation of ultrasound is:
ct
d
2
[1]
where: d = distance of the reflecting object
from the source/detector of ultrasound;
c = speed of the ultrasound;
t = round-trip time of the pulse, from
emission to reception.
What do we mean by ultrasound?
• Acoustic waves with frequencies above those
which can be detected by the human ear. In
practice, 20 kHz < f < 200 MHz.
• An acoustic wave is a propagating disturbance in a
medium, caused by local pressure changes at a
transducer.
• The molecules of the medium oscillate about their
resting (equilibrium) positions, giving rise to a
longitudinal waves.
• c  1540 m/s  6.5 μs/cm in most body tissues
• λ = c / f = 1.5 mm at 1 MHz.
Speed of sound
• The speed of sound is a constant in a given material (at a
given temperature), but varies in different materials:
• Material
Air
Water
Metal
Fat
Blood
Soft tissue
Velocity ( m/s)
330
1497
3000 - 6000
1440
1570
1540
Uses of ultrasound imaging
• Most widespread use is in
medical imaging
• Non-invasive, low risk
• Obstetrics, abdominal
problems, measurement of
blood flow and detection
of constrictions in arteries
and veins.
• Also used in nondestructive testing in
industry: e.g., cracks in
structures.
• Sonar, underwater
imaging (e.g., in
submarine echo-location Fig 2: Typical obstetric ultrasound scan
devices).
A-Mode
• Simplest form of ultrasound instrument
• Pulses of ultrasound in a thin beam are emitted
from a transducer into the body and encounter
interfaces between different organs.
• Some of the sound energy is reflected at each
stage and some continues through to be reflected
in turn by deeper organs.
• The returning pulses are detected by the
transducer and the amplitude of the signal is
displayed on an oscilloscope. If the time-base of
the scope is constant, then the distance across the
screen corresponds to the depth of the object
producing the echo, in accord with Eq. [1].
• A-mode imaging gives information very quickly
and involves a minimum of sophisticated
apparatus
• Weakness is that this information is onedimensional — i.e., along the line of the beam
propagation.
• Nowadays, this mode has been largely superseded
by the brightness B-mode (see later).
M-mode: first u/s modality to record
display moving echoes from the heart
Typical M-mode images. a. from left ventricle, b from
the mitral valve and c from the aortic valve
• A-mode still finds uses in ophthalmology, where
the simple structure of the eye makes it relatively
easy to interpret the echoes and where what is
required are straightforward but accurate
measurements of, for example, distance from the
lens to the retina.
• Even this very primitive instrument is not as
straightforward as it might seem. To understand
why, we need to look at a number of principles of
physics, engineering and signal processing.
Reflection coefficients
• Reflections occur when the incident wave
encounters a boundary between two materials with
different acoustic impedances.
• Acoustic impedance Z is the material property
which relates pressure changes p (in excess of
atmospheric) to the vibrational velocity u of the
particles in the medium.
[2]
p  Zu
• If we are looking at a single plane wave through a
substance with density ρ and speed of sound c,
then Z = ρc.
• When an incident plane wave, with amplitude pi,
travelling through a medium with acoustic
impedance Z1 hits a boundary with a second
material of impedance Z2 at normal incidence,
there is in general both a reflected wave pr and a
transmitted wave pt:
Z 2  Z1
pr 
pi ;
Z 2  Z1
2Z 2
pt 
pi
Z 2  Z1
[3]
Significance of reflection coefficients
• (i) Too little reflection is bad. pr / pi  0
Useful images occur only where there is a difference in
acoustic impedance. Tissues with strikingly different
properties in other respects may have similar acoustic
impedances. From Fig. 3, observe that there is virtually no
reflection at a transition from liver to spleen hence the two
tissues will not be delineated from each other.
• (ii) Too much reflection is bad. pr / pi  1
If difference in acoustic impedance is too high, then
virtually all the incident ultrasound will be reflected. This
means that the boundary is opaque to ultrasound. The organ
in question will show up very brightly, but there is an
inability to see through it to find out what is underneath
Reflection coefficients at various
tissue boundaries
Tendon/Fat
Water/Muscle
0
-10
-20
-30
Liver/Spleen
-40
-50 dB
(pr/ pi)2
1
0.1
0.01
Bone/Soft Tissue
Air/Solid
Air/Liquid
10-3
10-4
10-5
Muscle/Liver
Lens/Vitreous or
Aqueous Humour
Figure 4
Note that these are power reflection coefficients (see later).
Implications
• No ultrasound images of brain in vivo; skull
reflects ultrasound.
• Images of the heart have to be taken “round” the
ribs, which are also opaque.
• Finding the right “window” into the body is
important.
The ultrasound transducer must be “coupled” to the
body using a special gel. Before an ultrasound scan, a
thin layer of gel is smeared onto the skin. Why?
Answer
• The material from which transducers are made has
a very different acoustic impedance Ztransducer to that
of the body Ztissue and more importantly that of air
Zair.
• These large “mis-matches” between Ztransducer and
Ztissue and between Ztransducer and Zair mean that the
reflection coefficients at these interfaces are close
to -1.
• Little of the signal gets through at a transducertissue boundary (pr/pi  -0.86) and virtually none at
a transducer-air boundary
(pt/pi  - 0.9997).
• By applying the coupling gel, we exclude all air
from region between probe and body and the
worst case scenario of reflection from a
transducer-air boundary is avoided. The reflection
coefficient is still high (0.86), but imaging is
possible.
• Some manufacturers use impedance matching to
increase amount of transmitted radiation through
transducer-tissue interface. Inside the probe, there
is a matching layer of thickness λ/4 between
transducer and tissue. The acoustic impedance of
the matching material is approximately:
Zmatch  Ztransducer Ztissue
[4]
• The technique has analogues in optics (“blooming”
of lenses), electronics (coaxial transmission lines)
and quantum mechanics (scattering of particles by
potential wells).
• Note that this technique is not suitable in all cases
and, in particular, a λ/4 layer will match completely
only a single frequency of ultrasound.
(a)
(b)
Transducer
Soft Tissue
pi
“Matching” gel
Transducer
Soft Tissue
pi
pt
pt
pr
pr

|pt| << |pr|
|pt| >> |pr|
Fig 5: (a) A large degree of reflection occurs at the
interface between the ultrasound transducer and soft
tissue. (b) If the correct thickness of an appropriate
material is built into the probe, much improved
transmission can be obtained. Note that there is still a
thin gel layer (not shown) between the “matching” layer
inside the probe and the tissue. This has approximately
the same acoustic impedance as the soft tissue and is used
to exclude air.
What other aspects of wave
propagation are important?
• The formulae above are only strictly valid for an
infinite plane reflecting surface.
• In the body, there are many structures which are
much smaller than this (e.g., lung tissue is a fine
network of air-filled tubes). These give rise to a
whole series of interfaces, at random orientations,
and the reflections from these scatter the incident
wave.
• At a smaller scale where d << λ (e.g., red blood
cells), Rayleigh Scattering occurs and the degree
of scattering varies as f 4  1/λ4.
• This means that low frequency ultrasound
penetrates tissue better.
Absorption
• This is a phenomenon by which organised
vibrations of molecules (i.e. ultrasound) are
transformed into disorganised, random motion.
Acoustic energy  Heat
• The mechanisms for this transfer include fluid
viscosity, molecular excitations and chemical
changes. It is difficult to measure the proportion of
energy loss which occurs by scattering and the
proportion lost by absorption.
• The combined effect of absorption and scattering
may be written as
p0 ( x)  p0 (0) exp[( scatter   absorb ) x]
[5]
• This also applies to the peak oscillation velocity u0
and the amplitude of displacement a0 of the
particles.
• Attenuation is approximately proportional to
frequency, so that the depth of penetration goes
down as f rises.
• Instead of using amplitude, attenuation is often
measured in terms of a reduction in the power
density transported by the wave. Consider the
units of pu, where u is the particle vibration
velocity:
pressure  velocity = N/m2  m/s = (Nm)s-1/ m2 =
W/m2 = Power/unit area
• i.e., pu represents the power being transported by
the ultrasound through a unit area of the tissue
normal to the direction of propagation. It is often
also called the intensity of the ultrasound and is
represented by the symbol I.
• If we look at the power (intensity) attenuation, we
see that
I  pu  Re[ p0ei (t  kx ) ] . Re[u0ei (t  kx ) ]
 p0u0 cos2 (t  kx )
2
[6]
 I0 cos (t  kx ) .
• Now p0(x) = p0(0) e- αx and similarly for u0.
Hence
I 0 ( x )  I 0 (0) e
2x
[7]
The power density transported decays twice as
quickly as the vibration amplitude.
• Attenuation is often measured on a decibel scale,
where
 I ( x) 

Attenuatio n in dB  10 log 10 
 I (0) 
[8]
Diffraction
• Huygens’ Principle states that each point on a
wavefront can be regarded as a secondary source,
emitting spherical wavelets. The new overall wave
is found by summing the contributions from all the
individual wavelets.
• Thus, in an ultrasound imager, all points on the
surface of the transducer producing the ultrasound
act as a source of spherical wavelets.
• Also, when the ultrasound passes through an
aperture, each point on that aperture is like a
source of secondary wavelets; interference
between these wavelets gives rise to diffraction
effects.
• Diffraction becomes significant when the
apparatus dimensions and objects examined
become comparable with the radiation
wavelength. Thus acoustic diffraction (λ  0.1mm)
is a much more significant effect than optical
diffraction (λ  500nm) for biological tissues.
Practical ultrasound imaging
• Fig. 6 shows the block diagram of a practical Amode scanner.
• The new additions, when compared with the
simple diagram of Fig. 1, are concerned with the
practical problems in trying to use reflected
ultrasound, including:
• how the same probe both transmit pulses and
receive the echoes;
• how one deals with the signal attenuation by tissue
and;
• how the signal is displayed.
V
t
PRF generator
Reflecting objects
Pulse generator
Transducer
0
50
100
150
200
0
5 0
1 0 0
1 5 0
2 0 0
Protection circuit
70-80 dB
Variable gain
amplifier
(TGC)
TGC generator
40-50 dB
V(dB)
t
Demodulator
y
Display
’scope timebase
x
V
t
Fig 6. Block diagram of practical A-scanner. Not all A-mode scanners
include a demodulator. At each stage, the dynamic range values are
approximate and refer to the power range in the signal. Take the square root
(i.e., halve the dB value) for the corresponding amplitude ranges.
Master Clock (PRF Generator)
• This synchronises the various parts of the scanner
(e.g., transmitter, receiver, oscilloscope time-base)
so that each is triggered to act at the correct time.
• PRF stands for pulse repetition frequency, the
frequency at which clock pulses occur and at
which ultrasound pulses are sent out into the
sample.
Transmitter/Transducer/Receiver
• On the leading edge of each clock pulse, either a
momentary voltage step, or a short sinusoidal
burst of voltage is applied to the transducer.
• The transmitter which performs this must have a
short rise time, i.e., it must be able to go from zero
to its maximum voltage (100–200 V) very quickly
(typically < 25ns), in order to produce ultrasound
pulses with very high frequency components.
Time Gain Compensation (TGC)
• Problem: ultrasound is attenuated as it passes
through tissue.
• Thus, even for the same type of reflector, the
signal is less for deeper objects.
• This effect is very significant. Worked examples
show a typical a value of 0.15 cm–1, so on a
typical return trip of 10 cm, the signal is reduced
by exp (– 0.1510) = 0.22 compared with
reflections coming straight from the skin surface.
Solution to differential attenuation
• Amplify the later-arriving signals (i.e. the ones
from deeper in the tissue) more than those from
superficial reflections. i.e., change the receiver
gain with time to compensate for the echo
attenuation.
• This is achieved by making the gain of the
amplifier dependent on a control voltage.
Specifically, the input voltage is changed by the
TGC unit.
• Because of the logarithmic nature of the decrease
in signal, the TGC should increase the gain a
certain number of dB each ms.
Worked Example
• An ultrasound beam propagates in uniform liver tissue with a =
0.15 cm–1.
• If the speed of sound in the tissue is c = 1540 m/s, what should
be the rate of gain increase by the TGC?
• Since a = 0.15 cm–1 is the attenuation coefficient for
amplitude; the power attenuation is double this.
• Amplifiers are specified in terms of power, so 2a = 0.30 cm–1
is what we want.
• In terms of dB, we have –10 log10 (e – 0.3) = 1.3 dB cm–1
• So we want a gain increase of 1.3 dB for each cm of travel to
cancel out the differential attenuation.
1
• Now
1540 m / s  1 cm 
ms
154
1
ms  200 dB/ms
• This means that required TGC rate is 1.3 dB
154
• Clearly, a specialised amplifier is needed.
Principle of operation of time gain
compensation (TGC)
Variety of simple pre-programmed
shapes for increasing the gain
Gain / dB
60
40
Vclock
20
0
Vin
0
2
4
6
8
10
Depth / cm
Vcontrol
1/PRF
t
Vcontrol
Set of levels all adjustable by
operator for more flexibility
Variable gain
amplifier
(TGC)
t
Gain / dB
60
40
Vout
20
0
0
2
4
6
8
Depth / cm
Vout = G( Vcontrol ) . Vin
10
Fig 7
TGC Compensation and pitfalls
• In practice, tissue type varies with depth and the
situation is more complicated.
• The user is given a range of controls to vary the
TGC. The rate of increase of gain (i.e., d2G/dt2 )
varies with time and hence depth. This is not an
exact science!
• Notice, too, that by “tweaking” the time-gain
controls to get a better images, we lose the
information provided by the attenuation coefficient.
• By using this compensation we are “ignoring” the
physics of the situation. The fact that one might not
be able to see a particular boundary tells us
something about the properties of that boundary.
Demodulator
• At the output of the compression amplifier, the
echo signal mirrors that of the pulse, i.e., it
oscillates at the ultrasound frequency of several
MHz. The display is much easier to understand if
this high frequency modulation is removed.
• Another way of describing demodulation is to say
we want to change a signal oscillating at a high
frequency to a lower frequency. This is what we
saw in MRI.
The B-mode imager
• This is the commonest form of ultrasound
imaging, resembling radar images.
• A thin beam of ultrasound is scanned across the
object and the strength of the returned echoes is
displayed on the monitor.
• Notice that whilst in radar, full 360 coverage is
required, in medical ultrasound, where only the
body in front of the transducer is of interest, we
look at a limited “pie-shaped” sector.
2-dimensional imaging:
• Fire beam vertically, wait for echoes, store information &
then fire new line from neighbouring transducer etc in a
sequence of B-mode lines.
• In linear crystal array, electronic phased array shoots
parallel beams, with field as wide as probe length.
• Curved array creates a wider field than lateral probe
dimension, making possible creation of smaller footprint
for easier access through small windows at cost of reduced
lateral resolution as scan lines diverge.
Principle of B-scanning
0
50
100
150
200
Reflecting
Surfaces
0
50
100
150
200
Ultrasound
beam
Boundaries giving
rise to echoes
Other orientations
of ultrasound beam
Fig 8
Image Formed
To achieve footprint sufficiently small to get
access to heart between ribs, & with
sufficiently wide far field, beams have to
diverge from virtually same point. Hence
image has to be generated by single beam
from same point, deflected in different
angles to build a sector image.
• B-scan is “simply” an A-scan in which the
ultrasound beam is moved and the results are
spatially displayed. The ultrasound signal changes
the brightness of a spot on an oscilloscope screen
instead of amplitude of the trace in A-mode.
• What do we need to add to an A-scanner to turn it
into a B-scanner? As soon as we try to turn the idea
into a working system, we find a number of
problems lurking! How do we display the data
received? How do we make the beam sweep across
the sample? What do our data mean?
• Fig. 9 is a block diagram of a generic B-scanner.
Only three new items have been added: the coordinate generator, the video amplifier and the
beam-steering device.
V
t
PRF generator
Pulse generator
New
Beam steering
device
Protection circuit
Probe
Variable gain
amplifier
(TGC)
TGC generator
V(dB)
t
New
Demodulator
Compression and
Video Amplifier
Brightness
Co-ordinate
Generator
(x,y)
Display
Fig 9. Block diagram of a B-mode scanner
The Co-ordinate Generator
• This device is often also called the scan converter.
• It takes information about the instantaneous
orientation of the beam and turns it into the coordinates of a line on the display monitor.
• In simple systems, the CRT electron beam is
physically scanned up and down the desired line
(i.e., the co-ordinate generator acts as a variable
voltage source to the scope x- and y- plates).
• On more modern systems, the co-ordinate
generator gives the memory location in which
signal information is stored. The data is then
displayed on a monitor by a computer program.
Compression and Amplifier
• Even after passing through the TGC, the range of
signals in the data is still large.
• This is due to the range of reflector strengths in
the body — see Fig. 4.
• The compression amplifier transforms the data by
some rule Vout = f (Vin), which reduces the
dynamic range of the data (i.e., compresses the
scale).
• Typically, a 40–50 dB dynamic range for Iin (i.e., the ratio
Iin max/Iin min  104–105) is transformed to an output
dynamic range of 10 – 20 dB (10 – 100). Remember: take
the square root of these values to get the corresponding
voltage amplitude ranges.
• This allows low intensity echoes to be seen on the same
display as high intensity ones, i.e., strongly reflecting
organ boundaries and weakly reflecting internal structure
can be seen on the same image. A video monitor can
display only about 256 values simultaneously.
• This means that:
(i) a huge amount of information is lost as in the case of
the TGC;
(ii) one should not normally interpret B-mode image
intensities quantitatively.
The Beam-Steering Device
• This is what distinguishes the different types of
scanner.
• There are various levels of distinction. The most
basic is between static and real-time scanners.
Static B-Scanners
• The transducer is moved manually by the operator.
• The probe slides backwards and forwards over the
patient, changing its angle.
• The image is built up line by line. Each time, the
co-ordinates θ1, θ2 and θ3 tell the display where on
the screen to show the results. See Fig. 10
• The advantage of the system is that the operator
can choose which bits of the picture to update most
often and to tailor the scanning motion to view the
feature of interest from several different directions
• It is also very cheap.
Co-ordinate generator for
static B-scanner
Hinge



Probe
Patient
Fig. 10
Various types of beam steering
device for real-time scanners
Oil bath
Oscillating mirror
Ultrasound
beam
Rotating
transducers
Window
Fig 11
Oscillating transducer
Fixed transducer
However ...
• The scans take several seconds to build up and
form a complete picture. This is a problem if the
object in question moves in the meantime.
• Static B-scanners are not suitable for imaging of,
for example, a beating heart.
Real-Time Mechanical Scanners
• “Real time” scanners acquire anything from a few
frames (images) per second up to several hundred.
They are ideal for imaging motion.
• In a motorised scanner, the transducer is moved
mechanically by a motor.
• Because of the difficulties of maintaining contact
between the skin and a moving transducer, a larger
probe is used, which contains the transducer
“suspended” in a bath of oil, with a window to
allow the pulses to leave.
• There are several different designs, as shown in
Fig. 11. In all cases, the final device will depend
on obvious mechanical engineering questions like:
• How do you make a probe rock backwards and
forwards very fast? Can you make it do so
uniformly? How do you get leads to three
transducers on a ring without everything getting
tangled up when they rotate?
• The major disadvantage of this type of device is
that mechanical systems have an inherent speed
limit.
• The advantage is that there is no complicated (and
expensive) electronics.
Temporal resolution:
• To image moving objects frame rate is important,
related to speed of motion of object. Eye can
generally only see 25 FPS (video frame rate), giving
temporal resolution of ~ 40 ms. Higher frame rate
and new equipment offers possibility of replay at
lower rate, eg 50 FPS played at 25 FPS, doubling
effective resolution of eye.
• In quantitative measurement, whether based on
Doppler effect or 2D B-mode data, sufficient frame
rate is important to avoid undersampling (if one
undersamples at a certain frequency, then direction
of motion becomes ambiguous; more frequent
sampling will give correct direction).
• Temporal resolution limited by sweep speed,
which in turn is limited by speed of sound, echo
from deepest part of image having to return before
next pulse sent out. Sweep speed can be increased
by reducing number of beams in sector, or
decreasing sector angle. 1st option decreases lateral
resolution, 2nd decreases image field, so temporal
resolution cannot be increased without a trade off.
Electronic Steering: Transducer
Arrays
• We shall not go into any detail here, but the basic
principle is that a number of very small transducer
are placed into a line and are then fired separately.
• By “firing” (i.e., sending out a pulse from) the
transducers at different times, one can make
composite wave-fronts (Huygens Principle again!)
which mimic that given out from one of the
moving transducers above.
• The beam is scanned in a sector with a frame rate
of at least 20 Hz to minimise flicker. The probe
has no moving parts.
• Electronic beam steering is potentially much faster
than mechanical steering and also has the
advantage that the order of sampling of the
different lines is much more flexible.
• All modern scanners work this way.
Doppler Effect
• As velocity of sound in any medium constant, wave
propagates outwards in all directions with same
velocity, with centre at point of emission.
• As source moves, next wave is emitted from a point
further forward. Thus distance between wave crests
decreased in direction of motion/increased in
opposite direction.
• As distance between wave crests is equal to
wavelength, wavelength decreases (sound
frequency increases) in front of source/ increases
(sound frequency decreases) behind it. If source
stationary, effect on moving observer similar.
• In u/s, wave sent from stationary transducer, moving
blood or muscle firstly moving towards transducer
and then away thus Doppler shift approximately twice
as great. In case of reflected ultrasound, Doppler shift
is:
v
f D  2 f 0 cos 
c
where  is the angle between the direction of the
motion and the ultrasound beam, v is the blood or tissue
velocity, c is the sound velocity in tissue, f0 is the
transmitted frequency, fD is the Doppler shift of reflected
ultrasound.
• Basically, the Doppler effect can be used to
measure blood and tissue velocities from the
Doppler shift of reflected ultrasound:
fD c
v
2 f 0 cos 
Pulsed and continuous wave Doppler:
• Can use pulsed Doppler, where pulse sent out, and
frequency shift in reflected pulse measured at a
certain time. This will correspond to a certain
depth, i.e. velocity is measured at a specific depth,
which can be adjusted. The width is the same as
the beam width, and the length of the sample
volume is equal to length of the pulse.
• A problem in this is that Doppler shift is very
small compared to u/s frequency. This makes it
problematic to estimate the Doppler shift from a
single pulse, without increasing the pulse length
too far. A velocity of 100 cm/s with a ultrasound
frequency of 3.5 MHz results in a maximum
Doppler shift of 2.3 kHz.
• The solution is to shoot multiple pulses in the
same direction and produce a new signal with one
sample from each pulse.
• The pulsed modus results in a practical limit on
the maximum velocity that can be measured. In
order to measure velocity at a certain depth, the
next pulse cannot be sent out before the signal is
returned. The Doppler shift is thus sampled once
for every pulse that is transmitted, and the
sampling frequency is thus equal to the pulse
repetition frequency (PRF). Frequency aliasing
occurs at a Doppler shift that is equal to half of the
PRF.
fD = ½ PRF
Tissue Doppler
• The Doppler principle can be used both for blood flow and
tissue velocities.
• Main principle is that blood has high velocity (typically
above 50 cm/s, although also all velocities down to zero), but
low density, resulting in low intensity (amplitude) reflected
signals.
• Tissue has high density, resulting in high intensity signals,
but low velocity (typically below 20 cm/s).
• The difference in the applications used for the two sets of
signals is mainly differences in filtering, applying a high pass
filter in Doppler flow, and low pass filter in tissue Doppler
(although latter not absolutely necessary).
Magnetic Resonance
Imaging (MRI)
•
•
•
•
•
•
•
•
Introduction
Basic MR Physics
Advanced MR Physics
MR Techniques
Artefacts
Advanced Techniques
Instrumentation
MR Safety
MRI: Introduction
• In 1970s Lauterbur introduced concept of magnetic
field gradients, leading to images based on magnetic
resonance.
• By 1980s whole body magnets produced in UK,
permitting first in vivo images of human anatomy.
• An estimated 20 million scans now performed
worldwide annually.
• Provides excellent soft-tissue contrast; can be
acquired in any imaging plane; unlike CT, does not
involve ionising radiation.
• Imaging modality of choice in brain and spinal cord;
routinely used in many other clinical settings.
The Nobel Prize in Physiology
or Medicine 2003
Paul C. Lauterbur
Sir Peter Mansfield
• In 1971 Raymond Damadian showed that the nuclear magnetic
relaxation times of tissues and tumours differed, thus motivating
scientists to consider magnetic resonance for the detection of
disease.
• In 1973 the x-ray-based computerized tomography (CT) was
introduced by Hounsfield.
• This date is important to the MRI timeline because it showed
hospitals were willing to spend large amounts of money for
medical imaging hardware.
• Magnetic resonance imaging was first demonstrated on small
test tube samples that same year by Paul Lauterbur.
• He used a back projection technique similar to that used in CT.
• In 1975 Richard Ernst proposed magnetic resonance imaging
using phase and frequency encoding, and the Fourier Transform.
• This technique is the basis of current MRI techniques.
• In 1991, Richard Ernst was rewarded for his achievements in
pulsed Fourier Transform NMR and MRI with the Nobel Prize in
Chemistry.
• A few years later, in 1977, Raymond Damadian demonstrated
MRI called field-focusing nuclear magnetic resonance.
• In this same year, Peter Mansfield developed the echo-planar
imaging (EPI) technique.
• This technique was to be developed in later years to produce
images at video rates (30 ms / image).
• Edelstein and coworkers demonstrated imaging of the body
using Ernst's technique in 1980. A single image could be
acquired in approximately five minutes by this technique.
• By 1986, the imaging time was reduced to about five seconds,
without sacrificing too much image quality.
• The same year people were developing the NMR microscope,
which allowed approximately 10 mm resolution on
approximately one cm samples.
• In 1987 echo-planar imaging was used to perform real-time
movie imaging of a single cardiac cycle.
• In this same year Charles Dumoulin was perfecting magnetic
resonance angiography (MRA), which allowed imaging of
flowing blood without the use of contrast agents.
fMRI…
• In 1992 functional MRI (fMRI) was developed.
• This technique allows the mapping of the function of
the various regions of the human brain.
• Five years earlier many clinicians thought echoplanar imaging's primary applications was to be in
real-time cardiac imaging.
• The development of fMRI opened up a new
application for EPI in mapping the regions of the
brain responsible for thought and motor control.
• In 1994, researchers at the State University of New
York at Stony Brook and Princeton University
demonstrated the imaging of hyperpolarized 129Xe
gas for respiration studies.
NMR
• Felix Bloch and Edward Purcell, both of whom were
awarded the Nobel Prize in 1952, discovered the
magnetic resonance phenomenon independently in
1946.
• In the period between 1950 and 1970, NMR was
developed and used for chemical and physical
molecular analysis.
• For years major application in field of
spectroscopy; discerning chemical species from
inherent shift in resonant frequency exhibited by
nuclei; depends on chemical environment.
NMR
• NMR has become the preeminent technique for
determining the structure of organic compounds.
• Of all the spectroscopic methods, it is the only one for
which a complete analysis and interpretation of the
entire spectrum is normally expected.
• Although larger amounts of sample are needed than for
mass spectroscopy, NMR is non-destructive, and with
modern instruments good data may be obtained from
samples weighing less than a milligram.
NMR
• The nuclei of many elemental isotopes have a
characteristic spin (I).
• Some nuclei have integral spins (e.g. I = 1, 2, 3 ....),
some have fractional spins (e.g. I = 1/2, 3/2, 5/2 ....),
and a few have zero spin, I = 0 (e.g. 12C, 16O, 32S, ....).
• Isotopes of particular interest and use to organic
chemists are 1H, 13C, 19F and 31P, all of which have I =
1/2.
• Since the analysis of this spin state is fairly straight
forward, a general introductory discussion of NMR is
usually limited to these and other I = 1/2 nuclei.
Basic MR Physics: Nuclear Spin
& Behaviour in a Magnetic Field
• EM tells us that a current carrying conductor e.g. a piece of
wire, produces a magnetic field encircling it.
• When wire formed into a loop, field acts perpendicular to
surface area of loop.
• Analogous to this is field produced by negatively charged
electrons orbiting nucleus in an atom, or spinning charge of
nucleus itself.
• Spinning momentum of nuclear charge ('the spin') produces
small magnetic field referred to as magnetic moment.
• Under normal circumstances these moments have no fixed
orientation so no overall magnetic field.
• However, when nuclei placed in external magnetic field, for
example patient placed in MRI scanner, they begin to align
in given directions dictated by laws of QM.
Nuclear Spin & Behaviour in a
Magnetic Field
• In case of hydrogen nucleus (single proton with spin
quantum number, I = ½), two discrete energy levels (2I
+1) created;
• (i) a higher energy level where magnetic moments
oppose the external magnetic field, & (ii) a lower energy
level in which the nuclei aligned with magnetic field.
• Tiny majority of spins in latter energy state thereby
creating net magnetisation in direction of main magnetic
field.
• Population difference & therefore sensitivity of
technique, can be altered by reducing temperature or
increasing field, hence need for strong magnetic field;
for modern clinical scanners, between 0.5 and 3.0 Tesla.
Behaviour in a Magnetic Field
• Field referred to as B0 to distinguish from second field
described later.
• To put into context, 1 Tesla = 10,000 Gauss & Earth's
magnetic field varies between 0.3 - 0.7 Gauss.
• In terms of classical physics, when spin placed in a
magnetic field it precesses about that field in a motion
analogous to a spinning top.
• Frequency of precession governed by the Larmor equation,
ω0 = γB0.
• Constant of proportionality in equation is magnetogyric
ratio (or gyromagnetic ratio) with every 'MR visible'
nucleus having its own specific value [in units of Hz/T].
• For proton, in field strength of 1.5 T, the associated
frequency is about 63.8 MHz, which is in radio-frequency
(RF) range.
Figure: (left) A net magnetisation is produced following the
application of an external magnetic field causing a small majority of
spins to align in the direction of the applied field. (right) Each spin
precesses in a motion which follows the surface of a cone.
RF or Time-varying
Magnetic Field
• The quantum or classical physics descriptions are
entirely equivalent;
• in both cases there is a net magnetisation, M0, created
by the main magnetic field which is the basis of the
imaged signal.
• The net magnetisation can be considered in terms of
one big spin.
• In order to detect this signal a second magnetic field is
introduced referred to as B1. Two things are important
about this field: (i) it has to be applied perpendicular to
B0, and (ii) it has to be at the resonant frequency.
RF or Time-varying
Magnetic Field
• Appropriate RF coils are used to transmit B1, which
acts to tip the spins out of alignment with B0 and
towards the direction of the coil (i.e. out of the
longitudinal plane and towards the transverse plane).
• If the pulse is applied for long enough the spins are
flipped into the transverse plane and a 90° RF pulse is
said to have been applied.
• In the majority of MRI sequences this is the case.
• The RF pulse is then turned off and the signal can be
detected by the RF coil (either using the same one or a
second coil see Instrumentation ).
T1 Processes
• At equilibrium, the net magnetization vector lies along the
direction of the applied magnetic field Bo and is called the
equilibrium magnetization Mo. In this configuration, the Z
component of magnetization MZ equals Mo. MZ is referred to
as the longitudinal magnetization. There is no transverse (MX
or MY) magnetization here.
• It is possible to change the net magnetization by exposing the
nuclear spin system to energy of a frequency equal to the
energy difference between the spin states. If enough energy is
put into the system, it is possible to saturate the spin system
and make MZ=0.
• The time constant which describes how MZ returns to its
equilibrium value is called the spin lattice relaxation time (T1).
The equation governing this behavior as a function of the time
t after its displacement is:
Mz = Mo ( 1 - e-t/T1 )
• T1 is the time to reduce the difference between the
longitudinal magnetization (MZ) and its equilibrium
value by a factor of e.
• If the net magnetization is placed along the -Z axis, it
will gradually return to its equilibrium position along
the +Z axis at a rate governed by T1. The equation
governing this behaviour as a function of the time t
after its displacement is:
• Mz = Mo ( 1 - 2e-t/T1 )
• Again, the spin-lattice relaxation time (T1) is the time
to reduce the difference between the longitudinal
magnetization (MZ) and its equilibrium value by a
factor of e.
Relaxation Mechanisms
• At this point a peak in signal is detected which decays
very quickly called the Free Induction Decay (FID).
• The signal arises from the rotating magnetisation, it
decays due to relaxation which can be subdivided into
transverse or T2 decay and longitudinal or T1 recovery.
• T2 decay is the process whereby the millions of spins
begin to dephase.
• This is due to the individual spins 'seeing' local
differences in the magnetic field caused by interactions
between them, and they begin to precess at slightly
different rates resulting in an increasingly dispersed
distribution around 'the clock face' (see Figure below).
Figure: (left) Having been tipped into the transverse plane, the net
magnetisation begins to dephase (T2*). (right) Once fully dephased
the spins return to equilibrium (T1).
…Relaxation Mechanisms
• This is what causes the signal to decay at this point.
• In actual fact the spins dephase much quicker than the 'natural'
T2 as they also are subject to inhomogneities in the magnetic
field B0 causing the decay to be characterised by T2*.
• The second relaxation process governs the spins return to the
original equilibrium situation.
• Remember that at this stage, although B1 has been removed, the
main field B0 is always on and the spins begin to recover back to
alignment under its influence.
• The regrowth of magnetisation in this direction is characterised
by the T1 relaxation time and this is always much longer than the
corresponding value for T2.
T2 Processes
• In addition to the rotation, the net magnetization starts
to dephase because each of the spin packets making it
up is experiencing a slightly different magnetic field
and rotates at its own Larmor frequency. The longer
the elapsed time, the greater the phase difference.
Here the net magnetization vector is initially along
+Y. For this and all dephasing examples think of this
vector as the overlap of several thinner vectors from
the individual spin packets.
• The time constant which describes the return to
equilibrium of the transverse magnetization, MXY, is
called the spin-spin relaxation time, T2.
• MXY =MXYo e-t/T2
• Two factors contribute to the decay of transverse
magnetization.
1) molecular interactions (said to lead to a pure T2
molecular effect)
2) variations in Bo (said to lead to an inhomogeneous
T2 effect
The combination of these two factors is what
actually results in the decay of transverse
magnetization. The combined time constant is given
the symbol T2*. The relationship between the T2
from molecular processes and that from
inhomogeneities in the magnetic field is as follows:
1/T2* = 1/T2 + 1/T2inhomo
Typical relaxation times of
tissues in a field of 1 T
Material
Fat
Liver
Kidney
Spleen
White Matter
Grey Matter
CSF
Water
Ice
T1 (ms)
250
400
550
400
650
800
2000
3000
Very long
T2 (ms)
80
40
60
60
90
100
150
3000
Very short
T2 is always shorter than T1
Magnetic Field (T)
T1 of muscle (ms)
T2 of fat (ms)
0.15
330
170
0.30
440
190
0.50
550
210
1.0
730
240
1.5
870
260
Relaxation Time Summary
• The longitudinal relaxation time T1 is the decay
constant for the recovery of the z component of the
nuclear spin magnetization, Mz, towards its thermal
equilibrium value, Mz,eq. In general:
• The transverse relaxation time T2 is the decay
constant for the component of M perpendicular to B0,
designated Mxy,MT. For instance, initial xy
magnetisation at time zero will decay to zero (i.e.
equilibrium) as follows:
INVERSION RECOVERY (IR)
• An imaging sequence that involves successive 180˚ and 90˚
pulses, after which a heavily T1-weighted signal is obtained.
• The inversion recovery sequence is specified in terms of three
parameters, inversion time (TI), repetition time (TR) and echo
time (TE).
• The inversion time (TI) is the time period between the 180°
inversion pulse and the 90° excitation pulse.
• The repetition time (TR) is the amount of time that exists
between successive pulse sequences applied to the same slice. It
is delineated by initiating the first RF pulse of the sequence then
repeating the same RF pulse at a time t. Variations in the value
of TR have an important effect on the control of image contrast
characteristics. Short values of TR (< 1000 ms) are common in
images exhibiting T1 contrast, and long values of TR (> 1500
ms) are common in images exhibiting T2 contrast. TR is also a
major factor in total scan time.
Spin-echo
• Some of the signal can be recovered by the means of a
spin-echo.
• This involves the application of a refocussing RF pulse
such that the spins are flipped 180° so that the phaseposition of each spin has been inverted i.e. spins that
were precessing faster are now 'behind' spins that were
precessing at a slower rate.
• The actual spatial position of each spin has not altered,
in other words, following the application of the 180°
pulse the spins will still experience the same magnetic
field as before, so the precession rates are unaltered.
Spin-echo
• A finite time later the spins will have caught each
other up and a spin-echo is formed: this is a signal
peak which forms at the echo time, TE.
• The signal at this point is smaller than the original
peak of the FID because only the decay due to T2*
processes is recovered.
• The signal is now attenuated by natural T2
processes which cannot be recovered.
Summary: Spin Echo
• The spin-echo (SE) relates to the reappearance of the NMR signal after the FID
has apparently died away, as a result of the
effective reversal (rephasing) of the
dephasing spins by techniques such as
specific RF pulse sequences.
Image Contrast
• One of the great advantages of MRI is its excellent soft-tissue
contrast which can be widely manipulated.
• In a typical image acquisition the basic unit of each sequence
(i.e. the 90˚ & 180˚signal detection) is repeated hundreds of
times over.
• By altering the echo time (TE) or repetition time (TR), i.e.
the time between successive 90° pulses, the signal contrast
can be altered or weighted.
• For example if a long TE is used, inherent differences in T2
times of tissues will become apparent. Tissues with a long T2
(e.g. water) will take longer to decay and their signal will be
greater (or appear brighter in the image) than the signal from
tissue with a short T2 (fat).
Image Contrast
• In a similar manner TR governs T1 contrast.
• Tissue with a long TR (water) will take a long time
to recover back to the equilibrium magnetisation
value, so therefore a short TR interval will make
this tissue appear dark compared to tissue with a
short T1 (fat).
• When TE and TR are chosen to minimise both
these weightings, the signal contrast is only derived
from the number or density of spins in a given
tissue.
• This image is said to be 'proton-density weighted'.
To summarise:
T2-weighting requires long TE, long TR
T1-weighting requires short TE, short TR
PD-weighting requires short TE, long TR
Below are MRI brain examples with T2 (left) , T1
(centre), and proton density (right) weighting.
Fourier Transformation
• To understand how an image is constructed in MRI it is
first instructive to take a look at Fourier Transformation
(FT).
FT permits signal to be decomposed into a sum of sine
waves each of different frequency, phases and
amplitudes.
• S(t) = a0 + a1sin(ω1t + φ1) + a2sin(ω2t + φ2) + ...
• The FT of the signal in the time domain can be
represented in the equivalent frequency domain by a
series of peaks of various amplitudes.
• In MRI the signal is spatially encoded by changes of
phase/frequency which is then unravelled by performing
a 2D FT to identify pixel intensities across the image.
Slice Selection
• The Larmor equation states that the resonant frequency
is proportional to field strength.
• By applying linear changes in magnetic field (or
gradients) we can artificially change the resonant
frequency of the spins so that it is spatially dependent.
• To fully encode an image we need to discern the pixel
intensities in each of three dimensions.
• First we must consider how only a finite section or slice
of anatomy can be pre-selected by the scanner.
• From this point on we will consider how an axial image
is acquired (i.e. a cross-section perpendicular to the
main magnetic field direction).
Slice Selection
• In this case we perform slice selection along the zdirection: a gradient in this direction is turned on
such that it acts symmetrically about the centre of the
scanner (the isocentre.)
• In this way the resonant frequency is smaller than ω0
towards the patient's feet, unchanged at the isocentre,
and greater towards the head.
• By simultaneously using a shaped RF pulse
containing a finite bandwidth only a section of spins
either side of the isocentre is excited into the
transverse plane.
• The slice thickness or position can be varied by using
different gradient strengths or RF bandwidths.
Frequency Encoding
• Once the signal from the slice has been isolated the
remaining two in-plane dimensions need to be
encoded (in this case the 'x' and 'y' directions).
• One of the directions is encoded by changes of
frequency.
• Another gradient is turned on in (say) the x direction.
• Once again the centre of the slice remains unaltered
but to the left of this point the field and therefore
resonant frequency is smaller, to the right it is larger.
• Columns of pixels from left-to-right are therefore
discriminated in terms of frequency differences.
Phase Encoding
• It can be shown that a gradient applied in the ydirection to change frequency in this dimension would
not be sufficient to uniquely ascribe frequency to each
column and row of pixels.
• For the last dimension the signal is encoded in terms
of phase.
• This is not easy to understand: suffice it to say that a
number of gradients are needed to create phase
changes from row-to-row so that the FT is provided
with enough information to fully encode the final
image.
• What is more straightforward to understand, is how
gradients can alter phase as well as frequency.
Phase Encoding
• Clearly having applied a gradient, some spins will be
precessing faster than others.
• Once the gradient is removed the resonant frequency
is the same as it was before for all the spins (i.e. ω0).
• However, the spins will now be 'out of phase' with
each other.
• Any application of a gradient leads to alteration in
phase.
• In the real MR sequence, frequency-encoding and
slice-selection gradients have de-phasing 'lobes' to
prevent phase losses.
MRI Sequences
• We return to the spin-echo sequence.
• Now that the role of the gradients is
understood a real spin-echo sequence diagram
can be shown.
MRI Sequences
• The last line illustrates the evolution of the MR signal
(the FID immediately after the 90° pulse and the echo
at time, TE).
• Note that the repetition time is also labelled.
• Gradients are illustrated by rectangular blocks, the
area of which represents the amplitude and the sign
(i.e. positive or negative) dictated by the position
above or below the 'time' axis.
• In this example the phase encoding is in the y
direction and the phase encoding gradient (Gy) is
drawn as multiple lines to illustrate that the amplitude
of this changes each time the sequence is repeated.
MRI Sequences
• In contrast, frequency encoding (Gx) is performed
in one-go at the time of the signal detection.
• Note the de-phasing lobe, negative half of area,
which compensates for changes in phase, such that
at the time of the echo only a frequency change is
exhibited.
• Lastly, the slice-selection gradient (Gz) has to be
applied at the time of both RF pulses so that only
the spins within the slice of interest are excited
and refocussed.
• Note here too the use of a dephasing lobe.
MRI Sequences
• Total acquisition time for the spin-echo sequence is
given by product of TR, number of phase encoding
steps (number of pixels or matrix size in phase
direction) and number of averages i.e. the number of
times each exact part of sequence is repeated to
improve signal-to-noise (SNR).
• By recording the echo more than once the coherent
signal is additive but the incoherent noise cancels out.
• In fact, SNR is only proportional to the square root of
the number of averages i.e. doubling the averages,
increases the scan time by a factor of two, but
improves SNR by only 1.4.
MRI Sequences
• Multi-slice imaging is achieved by making use of
the time between the end of echo collection and the
next 90° excitation pulse (TR-TE), referred to as
dead time.
• In this period the next slice can be excited. The
scanner will determine how many more slices will
'fit' into the sequence. Another consideration is the
cross-talk (or more correctly 'cross-excitation')
which occurs between adjacent slices due to
imperfect slice profiles. This is accounted for by
leaving gaps or interleaving slices, so that even
slices are excited first followed by the odd slices.
Gradient Echoes
• A second type of echo important in MRI is the gradient echo.
• In contrast to the SE it is formed by applying a gradient and
then reversing the direction of this gradient. It does not require
a 180° RF pulse meaning that one advantage is faster imaging
time. However, the images are inherently T2* weighted as the
decay due to B0 inhomogeneities is not recovered, and they are
therefore prone to susceptibility artefacts.
• The use of gradient-echo imaging is primarily for rapid (short
TR) T1-weighted scans. The use of such short TRs makes it
prudent to use partial (non-90°) flip angles. The optimum flip
angle depends on both TR and T1 and is given by the Ernst
equation:
cos E = exp(-TR/T1)
• Note that for long TRs the optimum angle is 90° as expected.
Gradient Echoes
• The full GRE pulse sequence is:
Other Sequences
• The majority of the many other sequences in common use are
variations of the above two.
• For instance a Multi-Spin Echo simply uses more than one refocusing pulse to create separate echo images at increasingly
longer echo times. The sequence can be used to measure T2
('Carr-Purcell') by fitting the signal decay at each echo time.
• The corresponding diagram
for this sequence is:
Other Sequences
• A subtle but important difference in the Fast SpinEcho sequence is that some of the necessary phaseencoding steps are played out for each echo.
• What this means in real terms is that the total phaseencoding needed to be performed can be done much
faster.
• If the echoes are closely spaced, then the signal at
each echo can be used to form a single image at the
overall 'effective' echo time.
• The factor by which the sequence is speeded up
compared to a normal SE sequence is given by the
echo-train length (the number of echoes individually
phase-encoded).
Other Sequences
• The greater this number or the bigger the
spacing between the echoes, then the poorer
the quality of the final image. The diagram
for the FSE sequence is:
EPI and k-Space
• One final sequence worth considering is Echo-Planar
Imaging or EPI.
• To fully appreciate the utility of EPI we must first consider kspace. k-space is an array of numbers whose FT gives the MR
image. Each row (or line) in k-space corresponds to the echo
data collected with each application of the phase-encoding
gradient.
• The cells in k-space DO NOT equate one-to-one with the
pixels in the image; in fact each cell contains information
about every image pixel.
• Rows near to the centre of k-space correspond to low-order
(small amplitude) phase encoding steps and are therefore
related to the bulk of the image signal/contrast.
• The edges of k-space correspond to high-order gradient steps,
where the image detail can be found. To fully image an object
data in the whole of k-space must be collected.
EPI and k-Space
• By acquiring only part of k-space (or fewer
'lines') the scan will be much faster but
image quality will be compromised. To
illustrate this, consider the following images:
Figure: Examples of images obtained with full and partial k-space.
EPI and k-Space
• The image in the middle was acquired with full k-space,
while for the left hand image only the outer edges of k-space
were collected and as a result only the edges or detail are
present in the image.
• Conversely by acquiring only the central portion of k-space
(right image) more of the signal is produced but the detail is
missing.
• In normal imaging one line of k-space is collected and the
sequence is repeated with an increment of the phaseencoding gradient in order to acquire the next line 'up' and so
on.
• In EPI, the gradients are played out so that all lines of kspace are acquired in one TR (single-shot technique).
EPI and k-Space
• This means that the EPI sequence is extremely fast,
typically acquiring a slice every 50 ms.
• Usually fewer phase-encoding steps are collected compared to
a normal sequence (e.g. 64 instead of 256) so the images are
not of the same quality. Being so gradient intensive, EPI is
also prone to artefacts. Nevertheless, EPI is useful for
paedeatric studies or funtional MRI, were speed is essential.
MR Techniques: Contrast-Agents
• Although MR delivers excellent soft-tissue contrast
sometimes there is a need to administer exogenous
contrast usually an intravenous injection of some
paramagnetic agent, most commonly Gd-DTPA.
• Effect of agent is to shorten relaxation time of local spins
causing a decrease in signal on T2-weighted images & an
increase on T1-weighted images.
• Fig. shows brain images before/after contrast, allowing
disruptions in blood-brain barrier to be investigated.
Contrast-Agents
• The increased vascularity of tumours produces
a preferential uptake of contrast agent and the
technique can be used to better visualise these
from surrounding normal tissue.
• Furthermore if MR scans are repeatedly
acquired following the contrast injection, the
dynamic nature of contrast uptake can be
examined, which may improve the
differentiation of benign and malignant
disease.
Contrast-Agents
• Contrast agents are also increasingly being
used in MR angiography (see later in this
section).
• Superparamagnetic iron-oxide is used in the
liver, which improves tumour contrast by
decreasing T2 signal in normal tissue.
MR Techniques: Fat Suppression
• An important technique in MRI is fat suppression i.e.
removing the high signal fat component from the
image.
• There are many ways in which this can be achieved
but each method relies on either the resonant
frequency (chemical shift) or relaxation time
differences between water and fat.
• In the Chemical selective saturation method a
preparatory pulse sequence is acquired which utilises a
narrow bandwidth RF pulse to excite the fat peak
alone.
• The fat magnetisation is then deliberately dephased in
the transverse plane leaving only the water available
for subsequent detection.
Fat Suppression
• Another common method is the STIR sequence (Short TI
Inversion Recovery).
• This sequence uses a 180° RF pulse to invert water and fat
spins, then waits a given time (about 180 ms at 1.5 Tesla)
for the more rapidly-recovering fat peak to reach the null
point (i.e. the point at which it passess through the
transverse plane).
• At this point a 90° 'inspection' pulse flips the
magnetisation into the transverse plane so that the fat peak
is zero but the water peak, which still had a negative z
component, is measured.
•
Fat Suppression
• The disadvantage of this technique is that the
timing of the sequence has to be fixed, so the
weighting in the final image cannot be altered.
• SPIR, or Spectral Presaturation with Inversion
Recovery, is a combination of the two previous
methods, only the fat is excited and then
inverted as in the STIR method.
• The Dixon method involves acquiring images
with fat and water in or out of phase and
performing an image subtraction.
Fat Suppression
• An example of fat supression (using the first method) is given
in the Figure below for the breast.
Figure: Example of an axial breast image pre and post fat
suppression.
• The bright fat signal in the left has been removed in the right
image permitting a better visualisation of breast parenchyma.
MR Angiography
• One of the biggest growth areas for MRI is angiography.
• In normal circumstances flow effects cause unwanted
artefacts, but in MRA these phenomena are used
advantageously to permit the non-invasive imaging of the
vascular tree.
• Techniques can be generally divided into 'white' or 'black'
blood methods depending on whether moving spins
(blood) appear brighter or darker than stationary tissue.
• In high-velocity signal loss, blood which has moved inbetween the 90° and 180° pulses will not produce a signal
and appears darker than tissue which has experienced both
pusles.
MR Angiography
• Time-of-flight (TOF) makes use of entry slice
phenomenon (although strictly speaking high
velocity signal loss is also TOF).
• In this case, a short TR is used so that spins in the
imaging slice become quickly saturated (recover
to a constant value) but 'fresh' spins flowing into
this slice have their full magnetisation available
and therefore emit a high signal.
• This technique works best over thin sections and
when blood flow is perpendicular to the imaging
plane.
MR Angiography
• An increasingly used method is simply to take
advantage of the high signal from i.v. contrastagents.
• Although current clinical agents are extracellular,
and quickly distribute into the extravascular space,
accurate timing of the imaging sequence following
the contrast injection can provide excellent results.
• Good timing of the arterial bolus with the centre of
k-space acquisition is crucial to avoid artefacts. This
can be achieved using a small 'test bolus' or by
monitoring the contrast flow using rapid 2D images
before initiating the real sequence (Bolus tracking).
MR Angiography
• The image in Fig. is an example of what can
be achieved.
• Other techniques include stepping or moving
table MRA, where multiple table positions
(called stations) are used to image peripheral
arteries.
Artefacts
• Signal in image not present in object being scanned. Sometimes
caused by object, sometimes by limitations of scanner itself.
• Gibbs Ringing or Truncation Artefact This arises due to the
finite nature of sampling.
• According to Fourier theory, any repetitive waveform can be
decomposed into an infinite sum of sinusoids with a particular
amplitude, phase and frequency.
• In practice, a waveform (e.g. MRI signal) can only be sampled
or detected over a given time period and therefore the signal will
be under-represented.
• The artefact is prominent at the interface between high and low
signal boundaries and results in a 'ringing' or a number of
discrete lines adjacent to the high signal edge.
Artefacts
• Here an example of the artefact is seen in a test
object. The image matrix has been deliberately
reduced in the phase direction (64 pixels topto-bottom) compared to the frequency direction
(256, left-to-right) and the artefact is more
pronounced in the phase direction. The artefact
can be reduced by increasing the matrix size in
a given direction.
Phase-wrap or 'Aliasing'
• Aliasing can occur in either the phase or frequency
direction but is mainly a concern in the phase direction.
• It is a consequence of Nyquist theory: the sampling rate has
to be at least twice that of the highest frequency expected.
• Effect occurs whenever an object or patient anatomy is
outside selected field-of-view but within sensitive volume
of coil.
• For example, phase-encoding will be built up over period of
time with maximum phase shift between adjacent pixels
being 18˚.
• However, signal outside of the field-of-view is not
represented by an unambiguous phase and will be mismapped into the opposite side of in the final image (hence
the name 'wrap').
Phase-wrap or 'Aliasing'
• In frequency direction, this is avoided by
increasing sampling & use of high pass filters.
• By swapping direction of phase/frequency
encoding or using larger or rectangular fieldsof-view the effect can be avoided.
• In example, hand resting on top of chest has
appeared at bottom of image.
Motion Artefacts (Ghosting)
• Ghosting describes discrete or diffuse signal throughout
both the object and the background.
• It can occur due to instabilities within the system (e.g.
the gradients) but a common cause is patient motion.
• When movement occurs the effect is mainly seen in the
phase direction. This is because of the discrepancy
between the time taken to encode the image in each
direction.
• Frequency encoding, done in one go at the time of echo
collection, takes a few ms whereas phase encoding
requires hundreds of repetitions of the sequence, taking
minutes.
Motion Artefacts (Ghosting)
• Motion causes anatomy to appear in a
different part of the scanner such that the
phase differences are no longer consistent.
• Periodic motion e.g. respiratory or cardiac
motion can be 'gated' to the acquisition so
that the phase encoding is performed at the
'same' part of the cycle.
• This extends imaging time as the scanner
'waits' for the appropriate signal but is
effective in combating these artefacts.
Motion Artefacts (Ghosting)
• Modern scanners now so fast that 'breath-hold'
scans are replacing respiratory compensation.
• Non-periodic motion e.g. coughing, cannot
easily be remedied and patient co-operation
remains best method of reducing these artefacts.
• In this simple experiment a test object is moved
gently during the scan.
Motion Artefacts (Ghosting)
• The effect is dramatic and due to the fourier
transform nature of MRI, even this small
displacment has produced artefacts
throughout the image (the image is shown
twice with different 'window' settings to
enable the full extent of the artefact to be
seen).
Chemical Shift (1st Kind)
• This artefact arises due to the inherent differences in
the resonant frequency of the two main components of
an MR image: fat and water.
• It is only seen in the frequency direction. At 1.5 Tesla
there is approximately 220 Hz difference in the fatwater resonance frequency.
• If this frequency range has not been accommodated in
the frequency encoding (governed by the receiver
bandwidth and matrix size) then adjacent fat and water
in the object will artificially appear in separate pixels in
the final image.
• This leads to a characterisitic artefact of a high signal
band (where the signal has 'built up') and an opposite
dark band (signal void).
Motion Artefacts (Ghosting)
• An excellent example of this can be seen in an
egg. In this case the artefact (dark band towards
the top and bright band at bottom of image) is
several pixels wide.
Susceptibility
• The susceptibility of a material is the tendency
for it to become magnetised when placed in a
magnetic field.
• Materials with large differences in susceptibility
create local disturbances in the magnetic field
resulting in non-linear changes of resonant
frequency, which in turn creates image distortion
and signal changes.
• The problem is severe in the case of
ferromagnetic materials but can also occur at airtissue boundaries.
Susceptibility
• The example was acquired in a patient who had
permanent dental work. It did not create any
problems for patient but the huge differences in
susceptibility caused major distortions and
signal void in final image.
Other Artefacts
• An RF or zipper artefact (example) is caused by
a breakdown in the integrety of the RF-shielding
in the scan room. Interference from an RF
source causes a line or band in the image, the
position and width of which is determined by
the frequencies in the source.
Other Artefacts
• A Criss-cross or Herringbone artefact occurs
when there is an error in data reconstruction. In
the example for the breast two window levels
have been used to display the artefact clearly.
Other Artefacts
• A DC-offset leads to the central point artefact,
a bright spot at the centre of the image. When
the receiver amplifier is exceeded (Data
clipping or Overflow artefact) the resulting
image appears washed-out and ghost-like. Here
is an example in the brain.
Advanced Techniques: fMRI
• Functional MRI is a technique for examining brain activation which
unlike PET (Positron Emission Tomography) is non-invasive with
relatively high spatial resolution.
• The most common method utilises a technique called BOLD (Blood
Oxygen Level Dependent) contrast.
• This is an example of endogenous contrast, making use of inherent
signal differences in blood oxygenation content.
• In normal resting state, a high concentration of deoxyhaemoglobin
attenuates MR signal due to its paramagnetic nature.
• However, neuronal activity, in response to some task or stimulus,
creates local demand for O2 supply, increasing fraction of
oxyhaemoglobin causing signal increase on T2 or T2*-weighted
images.
• In a typical experiment the patient is subjected to a series of rest and
task intervals, during which MR images are repeatedly acquired.
Functional MRI
• The signal changes during this time course are then
examined on a pixel-by-pixel basis to test how well
they correlate with the known stimulus pattern.
• Pixels that demonstrate a statistically significant
correlation are highlighted in colour and overlayed
onto a greyscale MRI image to create an activation
map of the brain.
• The location and extent of activation is linked to the
type of task or stimulus performed, for example a
simple thumb-finger movement task will produce
activation in the primary motor cortex. An example of
this is shown in the Figure below.
Example of motor cortex activation in
a patient study
The subject was asked to perform a finger-thumb movement for 30 s,
repeated 3x, interspersed with 30 s periods of rest. Post-processing
established which pixels in brain had 'activated' during this task
(displayed in orange). Plot on right illustrates pattern of signal change
in this region (shown in blue) closely followed stimulus pattern (red).
fMRI is widely used as a research tool for examining brain function.
Diffusion-Weighted MRI
• Diffusion refers to random motion of molecules along a
concentration gradient.
• Diffusion-weighted MRI is another example of endogenous
contrast, using motion of spins to produce signal changes.
• The most common method employs Stejskal-Tanner bipolar
gradient scheme.
• Gradients with equal amplitude but opposite polarity are
applied over a given interval.
• Stationary tissue will be dephased and rephased equally,
whereas spins which have moved during the interval will suffer
a net dephasing and signal loss.
• By using gradients of sufficiently high amplitude the sequence
is sensitive to motion at the microscopic level.
Diffusion-weighted MRI
• Signal attenuation will depend on degree of
diffusion & strength & timing of gradients, the
latter expressed by gradient factor or b-factor.
• A diagram of this sequence indicating gradient
timings and b-factor expression is given below.
Diffusion-weighted MRI
• By acquiring images with different values of b (at least
2), a value for the apparent diffusion coefficient or
ADC, may be calculated.
• The experiment can be performed using diffusion
gradients in any direction.
• However, to obtain a complete 3-D description of
diffusion, a tensor has to be calculated, requiring a, b
= 0 image and 6 combinations of gradient pairs.
• This has the advantage of being able to discern
anisotropy due to preferential diffusion along
structures or fibres for example in white-matter tracts.
An example of this is given next.
Example of white-matter fibre
tracking in a normal subject
Although a wide area of research, the major clinical use for DWI at the
moment remains in stroke, where cell swelling caused by ischemia leads to
changes which can be demonstrated with DW-MRI much sooner than with
conventional MRI.
MR Spectroscopy
• MR Spectroscopy is a technique for displaying
metabolic information from an image.
• It relies on the inherent differences in resonant
frequency or the chemical shift that exists due to
different chemical environments.
• MR signal is measured and a spectrum plotting
amplitude against frequency is displayed.
• By using a standard reference the chemical species of
each peak can be determined.
• For proton MRS, the reference compound is
Tetramethylsilane (TMS).
MR Spectroscopy
• All chemical shifts are expressed as frequency
differences from this compound giving a fieldindependent parts per million (ppm) scale.
• Using this standard gives water its characteristic
peak at 4.7 ppm.
• Spectra of any 'MR visible' nucleus can be
obtained (e.g. 31P, 17F, 13C) so long as the RF
coil is tuned to the specific resonant frequency.
MR Spectroscopy
• In proton MRS, an important consideration is the
concentration differences between the metabolites of interest
and the overwhelming fat and water peaks which need to be
suppressed prior to acquisition.
• Since MRS relies on detecting frequency differences another
method is needed to localise the signal.
• Most methods use the intersection of three slice-select RF
pulse to excite a volume of interest (called a voxel).
• Multiple voxels can be acquired by using phase encoding in
each of the desired dimensions.
• This technique, called Chemical shift imaging, is useful in
isolating individual peaks and displaying the integrated area
as a colour scale to produce a metabolic map.
MR Spectroscopy
• The example in the Figure below illustrates
the potential clinical use of MRS.
Example of single voxel proton MRS in
normal and malignant brain tissue.
MR Spectroscopy
• The spectrum on the left was acquired in normal
healthy brain tissue and displays the characteristic
high N-Acetyl-Aspartate peak (NAA).
• On the right is a spectrum taken from a slightly
enlarged but otherwise normal looking part of the
Medulla, which did not show any enhancement with
Gadolinium.
• In this case the NAA peak is absent indicating loss
of viable tissue, and the choline peak is elevated,
which is indicative of the high cell proliferation in
tumours.
Instrumentation: the magnet
• Clearly the main component of the MR scanner is the magnet
itself.
• Some low field magnets are permanent or resistive but for all
scanners above 1.0 Tesla the magnet is superconductive i.e.
wound from an alloy (usually Nb-Ti) that has zero electrical
resistance below a critical temperature.
• To maintain this temperature the magnet is enclosed and cooled
by a cryogen containing liquid helium (sometimes also nitrogen)
which has to be topped-up on a monthly basis.
• Imperfections in the superconductive windings (soldered joins)
means that the scanner will lose 5-10 G per year.
• Far more serious is a quench when the magnet suddenly loses its
superconductivity and begins to heat up causing the cryogens to
boil and escape. Vents attached to the top of the scanner (see
pictures below) ensure that this happens safely.
Figure: 1.5 Tesla GE Signa scanner. Also shown
(left hand edge) is copper-lined door which acts as
an RF-screen. Any breakdown in this shielding
results in RF artefacts.
Figure: a Philips intera 1.5 Tesla system. The
shorter bore of this system is immediately
apparent. Also shown in this picture is the RF
head coil on the patient bed.
Other types of whole-body scanner include open
systems which use vertically orientated field
designs to reduce claustrophobia or enable surgical
procedures to be carried out.
RF Coils
• As covered earlier, RF coils are needed to transmit and/or
receive the MR signal.
• In order to optimise signal-to-noise ratio (SNR), the RF coil
should cover only the volume of interest.
• This is because the coil is sensitive to noise from the whole
volume while the signal comes from the slice of interest.
• To this end there are many types of RF coil with trade-offs in
terms of coverage and sensitivity.
• The most homogenous coils are of a 'birdcage' design. Examples
of these include the head and body coils.
• Both these coils act as transceivers i.e. they transmit and receive.
• The body coil is integrated into the scanner bore and cannot be
seen by the patient.
• The head coil, being smaller in size provides better SNR.
RF Coils
• Surface coils, as the name suggests, are used for
imaging anatomy near to the coil.
• They are simple loop designs and have excellent
SNR close to the coil but the sensitivity drops off
rapidly with distnace from the coil.
• These are only used as receivers, the body coil acting
as the transmitter.
• Multiple loops can be connected into a phased array
design, combining the excellent SNR with greater
volume coverage.
RF Coils
• Quadrature or circularly-polarised coils
comprise two coils 90° apart to improve SNR
by a factor of 2½. Some examples of common
RF coils can be viewed here.
Gradients
• The principle role of the gradient coils are to produce
linear changes in magnetic field in each of the x,y and
z directions.
• By combining gradients in pairs of directions, oblique
imaging can be performed.
• Gradient specifications are stated in terms of a slew
rate which is equal to the maximum achievable
amplitude divided by the rise time.
• Typical modern slew rates are 150 T/m-s.
• The gradient coils are shielded in a similar manner to
the main windings. This is to reduce eddy currents
induced in the the cryogen which would degrade image
quality.
Safety
• Although MRI is considered to be completely safe, it is
instructive to consider how the scanner interacts with
the patient.
• To put this section into historical context, in 1980 there
were concerns about using field strengths as little as
0.35 T but within 6 years this 'safe' limit had moved up
to 2.0 T.
• Similarly, gradient performances were limited to 3 T/s
in the mid-1980s whereas today MRI is routinely
performed with gradients exceeding 50 T/s.
• What follows is a summary of each particular safety
issue associated with MRI.
Static Field Effects
• The most obvious safety implication is the strength of
the magnetic field produced by the scanner.
• There are three forces associated with exposure to this
field: a translational force acting on ferromagnetic
objects which are brought close to the scanner (projectile
effect), the torque on patient devices/implants, and
forces on moving charges within the body, most often
observed as a superposition of ECG signal.
• In the main, sensible safety precautions and the
screening of patients means that there are seldom any
problems.
Static Field Effects
• Of major concern is the re-assessment of medical
implants and devices deemed safe at 1.5 Tesla which
may not have been tested at higher fields.
• This is becoming an issue as 3.0 T scanners become
more commonplace.
• The extension of the magnetic field beyond the scanner
is called the fringe field.
• All modern scanners incorporate additional coil
windings which restrict the field outside of the imaging
volume.
• It is mandatory to restrict public access within the 5
Gauss line, the strength at which the magnetic field
interfers with pacemakers.
Gradient Effects
• These come under the term 'dB/dt' effects referring to
the rate of change in field strength due to gradient
switching.
• The faster the gradients can be turned on and off, the
quicker the MR image can be acquired.
• At 60 T/s peripheral nerve stimulation can occur, which
although harmless may be painful.
• Cardiac stimulation ocurs well above this threshold.
• Manufacturers now employ other methods of increasing
imaging speed (so called 'parallel imaging') in which
some gradient encoding is replaced.
RF Heating Effects
• The repetitive use of RF pulses deposits energy which
in turn causes heating in the patient.
• This is expressed in terms of SAR (specific absorption
rate in W/kg) and is monitored by the scanner
computer.
• For fields up to 3.0 Tesla, the value of SAR is
proportional to the square of the field but at high fields
the body becomes increasingly conductive
necessitating the use increased RF power.
• Minor patient burns have resulted from use of high
SAR scans plus some other contributory effect, e.g.
adverse patient or coil-lead positioning, but this is still
a rare event.
Noise
• The scans themselves can be quite noisy.
• The Lorentz forces acting on the gradient coils due to
current passing through them in the presence of the
main field causes them to vibrate.
• These mechanical vibrations are transmitted through to
the patient as acoustic noise.
• As a consequence patients must wear earplugs or head
phones while being scanned.
• Again, this effect (actually the force on the gradients)
increases at higher field and manufactures are using
techniques to combat this including lining the scanner
bore or attaching the gradient coils to the scan room
floor thereby limiting the degree of vibration.
Claustrophobia
• Depending on the mode of entry into the scanner (e.g.
head first or feet first) various sites have reported that
between 1 % and 10 % of patients experience some
degree of claustrophobia which in the extreme cases
results in their refusal to proceed with the scan.
• Fortunately, modern technology means that scanners
are becoming wider and shorter drastically reducing
this problem for the patient.
• In addition, bore lighting, ventilation as well as the
playing of music all help to reduce this problem to a
minimum.
Bioeffects
• There are no known or expected harmful effects on
humans using field strengths up to 10 Tesla.
• At 4 Tesla some unpleasant effects have been
anedoctally reported including vertigo, flashing lights
in the eyes and a metallic taste in the mouth.
• Currently pregnant women are normally excluded from
MRI scans during the first trimester although there is
no direct evidence to support this restriction.
• The most invasive MR scans involve the injection of
contrast agents (e.g. Gd-DTPA). This is a colourless
liquid that is administered i.v. and has an excellent
safety record. Minor reactions like warm sensation at
the site of injection or back pain are infrequent and
more extreme reactions are very rare.