ph3-mi (medical imaging) course lecturer: david bradley office 18bc04. extension 3771 e-mail:...
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PH3-MI (Medical Imaging)
• 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:
2
2
)(
)(
PhosphorOutputofDiameter
PhosphorInputofDiameterGainonMinificati
• 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
35 mm Camera
Conventional Video System
15 - 18 5 lp/mm 4.2 lp/mm 2.5 lp/mm 1.5 - 1.3 lp/mm
23 - 25 4.2 lp/mm 3.7 lp/mm 2.2 lp/mm 1.0 - 0.9 lp/mm
General Principles• Resolution
Ability to discern two points close together
Unresolved Resolved
General Principles• Contrast
Ability to discern interesting object from noise or other tissues
Good ContrastPoor 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
[1]
where I0 is intensity measured at depth zero.
)exp()( 0 dIdI
• 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
[2]
• For the limit Δy 0, N , this becomes
[3]
)exp()exp()exp()( 3210 yyyIynI
n
ii yI
10 exp
sampleacross
0 )(exp dyyμII
Fig 1: Schematic diagram of a 1st generation CT scanner
X-ray source
X-ray detector
x
y
x
y
“Real” space coordinate
system (x, y)
Source and detector slide in tandem on gantry
x
y
x
y
Rotated coordinate system (x, y)
(a) (b)
(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 :
[4] dyyxIxI ),(exp)( 0
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
[5]
cossin
sincos
yxy
yxx
r
r
Figure 2: Relationship between Real Space and Radon Space
x
yy
x
Typical path of X-rays through sample, leading to detected intensity I(x)
x
Convert I(x) to (x)
Store the result (x) at the point (x ) in Radon space
Real (Image) Space Radon Space
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.
• Hence, the “projection signal” when the gantry is at angle φ is
[6]
• We define the Radon transform as
[7]
dyyxIxI ),(exp)( 0
0sample
)(ln),()(
I
xIdyyxx
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.
y
x x
Real (Image) Space Radon Space
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
[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.
)cos(sincos 000 Ryxx
Reconstruction of CT images
• This is performed by a process known as back-projection, 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
y
x x
Real (Image) Space Radon Space
0Beam path corresponds to peak in projection, with result stored in Radon space
Entire x-profile (i.e., set of projections for all values of xf ) is stored as a row in Radon space
(a)
Fig 4b. Projections at different angles correspond to different rows
of the sinogram
x
Radon Space
y
x
0 y
x
0
y
x
30 y
x
y
x
y
x
30
y
x
45 y
x
y
x
y
x
45
y
x
90 y
x
y
x
y
x
90
(b)
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 non-
filtered 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
Object
Image
Filtered profile
Image
Profile
Forward Projection
Filtered Back-Projection
Filtered Projection
Back- Projection
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 (~1975)
•Single X-ray Pencil Beam•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 fan-beam 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
•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
X-rays CT - Electron Beam 4th Generation
CT Numbers
Linear attenuation coefficient of each tissue pixel is compared with that of water:
w
wtNoCT
1000.
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
7
6
5
4
3
2
1
0
224-255
192-223
160-191
128-159
96-127
64-95
32-63
0-31
Intensity
159
7
6
5
4
3
2
1
0
Intensity
128 2550
Pixel Value
Int Int Int
Pixel Value Pixel ValuePixel Value
General Principles• Image Display - Look up tables
Logarithmic Exponential Inverse Linear
Window
General Principles• Image Display - Look up tables
Threshold
Intensity
Pixel Value
Colour Look-up table
Same image windowed to different levels
Brain image
Windowing and window level
Ring artefact in a third-generation scanner
Detail-contrast diagram for a CT scanner
Patient Dose in CT
dose
sizeectableimumcontrastectableimumthicknessslice
elyalternativordose
sizepixelnoiserelativethicknessslice
1detmindetmin
,,
1
32
32
Radiation RisksModality Typical Radiation
Dose (mSv)Plain x-ray 0.02 - 5
CT 10
MRI -
Gamma camera 2 – 20
PET 2 - 10
Ultrasound -
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
Disease Present
Disease Absent
Test Positive
True Positives (TP)
False Positive (FP)
Test Negative
False Negatives (FN)
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
0 50 100 150 200
0 5 0 1 0 0 1 5 0 2 0 0
Reflector
Emitted pulse
Lower amplitudereflected pulse
c
c
d
Transducer
c
Wavefronts
Rarefaction
Compression
Fig 1. Longitudinal waves in gas
• The fundamental equation of ultrasound is:
[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.
dct
2
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 Velocity ( m/s)Air 330Water 1497Metal 3000 - 6000Fat 1440Blood 1570Soft tissue 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 non-destructive testing in industry: e.g., cracks in structures.
• Sonar, underwater imaging (e.g., in submarine echo-location devices).
Fig 2: Typical obstetric ultrasound scan
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 one-dimensional — 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:
[3]itir p
ZZ
Zpp
ZZ
ZZp
2 ;
12
2
12
12
Significance of reflection coefficients
• (i) Too little reflection is bad. pr / pi 0Useful 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 1If 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
0 -10 -20 -30 -40 -50
1 0.1 0.01 10-3 10-4 10-5
(pr/ pi)2
dB
Air/SolidAir/Liquid
Bone/Soft Tissue
Tendon/Fat
Lens/Vitreous orAqueous Humour
Water/Muscle
Muscle/Liver
Liver/Spleen
Note that these are power reflection coefficients (see later).
Figure 4
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 transducer-tissue 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:
[4]Z Z Zmatch transducer tissue
• 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.
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
[5]
• This also applies to the peak oscillation velocity u0 and the amplitude of displacement a0 of the particles.
p x p x0 0 0( ) ( ) ) ] exp[ ( scatter absorb
• 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 [6]I pu p e u e
p u t kxI t kx
i t kx i t kx
Re[ ] Re[ ]cos ( )
cos ( )
( ) ( )0 0
0 02
02
.
.
• Now p0(x) = p0(0) e- αx and similarly for u0. Hence
[7]
• Attenuation is often measured on a decibel scale, where
[8]
I x I e x0 0
20( ) ( )
The power density transported decays twice as quickly as the vibration amplitude.
)0(
)(log 10dBin n Attenuatio 10 I
xI
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 A-mode 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.
PRF generator
Demodulator
TGC generator
Protection circuit
Variable gainamplifier
(TGC)
’scope timebase
Pulse generator
0 50 100 150 200
0 5 0 1 0 0 1 5 0 2 0 0
Transducer
Display
Reflecting objects
x
y
70-80 dB
40-50 dB
V
V
V(dB)
t
t
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 (– 0.1510) = 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. • Now
• This means that required TGC rate is • Clearly, a specialised amplifier is needed.
ms 154
1cm 1 s /m 1540
dB/ms 200 ms 154
1dB 3.1
Principle of operation of time gain compensation (TGC)
0 2 4 6 108
Depth / cm
Gai
n /
dB
20
0
40
60
Set of levels all adjustable by operator for more flexibility
0 2 4 6 108
Depth / cm
Gai
n /
dB
20
0
40
60
Variety of simple pre-programmed shapes for increasing the gain
Vclock
tVcontrol
t
1/PRF
Variable gainamplifier
(TGC)
Vcontrol
Vout
Vin
Vout = G( Vcontrol ) . Vin
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
ReflectingSurfaces
Boundaries giving rise to echoes
Other orientationsof ultrasound beam
Ultrasoundbeam
Image Formed
Fig 8
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 co-ordinate generator, the video amplifier and the beam-steering device.
PRF generator
Demodulator
TGC generator
Protection circuit
Variable gainamplifier
(TGC)
Co-ordinateGenerator
Pulse generator
(x,y)
Brightness
V
V(dB)
t
t
Display
Video Amplifier
Probe
Beam steeringdevice
New
New
Compression and
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 co-ordinates 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
Patient
Probe
Fig. 10
Various types of beam steering device for real-time scanners
Window
Ultrasound beam
Rotatingtransducers
Oil bath
Oscillating transducer Fixed transducer
Oscillating mirror
Fig 11
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:
where is the angle between the direction of the motion and the ultrasound beam, v is the blood or tissuevelocity, c is the sound velocity in tissue, f0 is the transmitted frequency, fD is the Doppler shift of reflectedultrasound.
cos2 0 c
vffD
• Basically, the Doppler effect can be used to measure blood and tissue velocities from the Doppler shift of reflected ultrasound:
cos2 0f
cfv D
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 echo-
planar 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/T
2
• 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 effectThe 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 T1 (ms) T2 (ms) Fat 250 80
Liver 400 40 Kidney 550 60 Spleen 400 60
White Matter 650 90 Grey Matter 800 100
CSF 2000 150 Water 3000 3000
Ice Very long Very short
T2 is always shorter than T1
Magnetic Field (T) 0.15 0.30 0.50 1.0 1.5 T1 of muscle (ms) 330 440 550 730 870 T2 of fat (ms) 170 190 210 240 260
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 phase-position 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 re-appearance 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 z-
direction: 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 y-direction 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 re-
focusing 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 Spin-Echo sequence is that some of the necessary phase-encoding steps are played out for each echo.
• What this means in real terms is that the total phase-encoding 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 k-
space. 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 phase-encoding gradient in order to acquire the next line 'up' and so on.
• In EPI, the gradients are played out so that all lines of k-space 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 in-between 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. contrast-agents.
• 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 top-to-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 mis-mapped 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 fields-of-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 fat-water 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 air-tissue 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 field-independent 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.