PH3MI Medical Imaging

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PH3-MI (Medical Imaging)

• Course Lecturer David Bradley
• Office 18BC04. Extension 3771
• E-mail d.a.bradley_at_surrey.ac.uk
• Content an introduction to imaging using
  ionising radiations, focusing on CT use of
  non-ionising radiations, focusing on ultrasound
  imaging and MRI.

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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.

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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.

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Detail detectability test phantoms
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Detail-detectability
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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.

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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.

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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.

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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.

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Image Intensifier
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• 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.

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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 46 lp/mm. Spatial resolution of system
  depends on other imaging components in imaging
  chain.

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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.

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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

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• 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 

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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.

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General Principles

• Resolution

Ability to discern two points close together
Unresolved
Resolved
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General Principles

• Contrast

Ability to discern interesting object from noise
or other tissues
Good Contrast
Poor Contrast
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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.

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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.

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Principles of x-ray attenuation

• Attenuation CT imaging based on Beers 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.

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• Suppose we now consider a set of blocks of
  different material, each of width ?y. The x-ray
  intensity measured at the exit of the set of
  blocks is 2
• For the limit ?y ? 0, N ? ?, this becomes
• 3

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Fig 1 Schematic diagram of a 1st generation CT
scanner
(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.
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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

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• EMI CT head scanner (Mayo Clinic, Rochester,
  Minn, circa 1973)

and an 80 x 80-matrix head CT image obtained with
it.
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General Principles

• Image Display - Pixels and voxels

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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 f by xf and the
  perpendicular axis by yf.
• Clearly, we may relate our (xf, yf) coordinates
  to the coordinates in the un-rotated lab frame by
  5

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Figure 2 Relationship between Real Space and
Radon Space
Highlighted point on right shows where the value
?f (xf) created by passing the x-ray beam through
the sample at angle f and point xf is placed.
Note that, as is conventional, the range of f is
-p / 2, p / 2, since the remaining values of f
simply duplicate this range in the ideal case.
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• Hence, the projection signal when the gantry is
  at angle f is
• 6
• We define the Radon transform as
• 7

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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 xf and f . At the general
  point (xf, f), we store the result of the
  projection ?f(xf).
• Taking lots of projections at a complete range of
  xf and f fills Radon space with data, in much
  the same way that we filled Fourier space with
  our 2-D MRI data.

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Fig 3. Sinograms for sample consisting of a small
number of isolated objects.
In this diagram, the full range of f is -p, p
is displayed.
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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 f, all locations xf lead to
  ?f(xf) 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 xf   x0 cos f y0 sin f.

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• 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 f0 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 f0). See Fig 3 for an illustration of this.

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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 f. Note how in Fig 3, the value of the
  Radon transform ?f(xf) 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.

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Fig 4a. Relationship of 1-D projection through
the sample and row in sinogram
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Fig 4b. Projections at different angles
correspond to different rows of the sinogram
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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.
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Reconstruction of CT images (continued)

• Place the sinogram row at an angle f in real
  space. Then smear it out evenly all the way
  along the yf -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.

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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.

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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.
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General Principles- Filtered BP
Forward Projection
Back- Projection
Filtered Back-Projection
Filtered Projection
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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.

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• 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.

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Four generations of CT scanner
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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

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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

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X-rays CT - 3rd Generation (1985)
The General Electric CTi CT scanner (1999)
Scott White Texas A M University College of
Medicine
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X-rays CT - 3rd Generation
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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

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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/
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X-rays CT - Multi Slice
Latest Developments - Spiral, multislice CT?
Cardiac CT
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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
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CT Numbers

• Linear attenuation coefficient of each tissue
  pixel is compared with that of water

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• 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.

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Windowing in CT
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General Principles

• Image Display - Look up tables

Intensity
159
128
255
0
Pixel Value
Int
Int
Int
Pixel Value
Pixel Value
Pixel Value
Logarithmic
Exponential
Inverse Linear
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General Principles

• Image Display - Look up tables

Same image windowed to different levels
Colour Look-up table
Brain image
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Windowing and window level
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Ring artefact in a third-generation scanner
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Detail-contrast diagram for a CT scanner
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Patient Dose in CT
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Radiation Risks
Risk of fatal cancer - 1 in 20,000 per mSv per
year
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CT and corresponding pixels in image
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• Simple numerical
• example

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The decision/confusion matrix
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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

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sensitivity and specificity 2 x 2 table below
labeled with test result on lhs, disease status
on top
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Sensitivity vs false-positive rate line D is
worthless, B is good, A is ideal
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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)

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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.

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Basic principles
Fig 1. Longitudinal waves in gas
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• 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.

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What do we mean by ultrasound?

• Acoustic waves with frequencies above those which
  can be detected by the human ear. In practice, 20
  kHz lt f lt 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
• ? c / f 1.5 mm at 1 MHz.

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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 1497Me
  tal 3000 - 6000Fat 1440Blood 1570Soft
  tissue 1540

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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
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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.

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• 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).

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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
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• 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.

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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

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• If we are looking at a single plane wave through
  a substance with density ? and speed of sound c,
  then Z ?c.
• 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

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Significance of reflection coefficients

• (i) Too little reflection is bad. pr / pi ? 0
• Useful images occur only where there is a
  difference in acoustic impedance. Tissues with
  strikingly different properties in other respects
  may have similar acoustic impedances. From Fig.
  3, observe that there is virtually no reflection
  at a transition from liver to spleen hence the
  two tissues will not be delineated from each
  other.
• (ii) Too much reflection is bad. pr / pi ? ?1
• If difference in acoustic impedance is too high,
  then virtually all the incident ultrasound will
  be reflected. This means that the boundary is
  opaque to ultrasound. The organ in question will
  show up very brightly, but there is an inability
  to see through it to find out what is underneath

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Reflection coefficients at various tissue
boundaries
Figure 4
Note that these are power reflection coefficients
(see later).
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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?
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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).

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• 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 ?/4
  between transducer and tissue. The acoustic
  impedance of the matching material is
  approximately
• 4

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• 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 ?/4 layer will match
  completely only a single frequency of ultrasound.

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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.
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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.

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• At a smaller scale where d ltlt ? (e.g., red blood
  cells), Rayleigh Scattering occurs and the degree
  of scattering varies as f 4 ? 1/?4.
• This means that low frequency ultrasound
  penetrates tissue better.

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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.

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• 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.

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• 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

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• 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

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• Now p0(x) p0(0) e- ax and similarly for u0.
• Hence 7
• Attenuation is often measured on a decibel scale,
  where
• 8

The power density transported decays twice as
quickly as the vibration amplitude.
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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.

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• Diffraction becomes significant when the
  apparatus dimensions and objects examined become
  comparable with the radiation wavelength. Thus
  acoustic diffraction (? ? 0.1mm) is a much more
  significant effect than optical diffraction (? ?
  500nm) for biological tissues.

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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.

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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.
107
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.

108
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 (100200 V) very
  quickly (typically lt 25ns), in order to produce
  ultrasound pulses with very high frequency
  components.

109
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 cm1, so on a
  typical return trip of 10 cm, the signal is
  reduced by exp ( 0.15?10) 0.22 compared with
  reflections coming straight from the skin surface.

110
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.

111
Worked Example

• An ultrasound beam propagates in uniform liver
  tissue with a 0.15 cm1.
• 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 cm1 is the attenuation
  coefficient for amplitude the power attenuation
  is double this.
• Amplifiers are specified in terms of power, so 2a
  0.30 cm1 is what we want.
• In terms of dB, we have 10 log10 (e 0.3)
  1.3 dB cm1
• 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.

112
Principle of operation of time gain compensation
(TGC)
Fig 7
113
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.

114
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.

115
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.

116
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.

117
Principle of B-scanning
Fig 8
118

• 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.

119

• 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?

120

• 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.

121
Fig 9. Block diagram of a B-mode scanner
122
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.

123
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).

124

• Typically, a 4050 dB dynamic range for Iin
  (i.e., the ratio Iin max/Iin min ? 104105) 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.

125
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.

126
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 ?1, ?2 and ?3 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.

127
Co-ordinate generator for static B-scanner
Fig. 10
128
Various types of beam steering device for
real-time scanners
Fig 11
129

• 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.

130
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.

131

• 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.

132
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). 

133

• 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.

134
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.

135
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136
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137
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138

• 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.

139
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.

140

• 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 tissue velocity, c is the sound velocity
in tissue, f0 is the transmitted frequency, fD
is the Doppler shift of reflected ultrasound.
141

• Basically, the Doppler effect can be used to
  measure blood and tissue velocities from the
  Doppler shift of reflected ultrasound

142
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.

143

• 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.

144

• 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

145
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).

146
Magnetic Resonance Imaging (MRI)

• Introduction
• Basic MR Physics
• Advanced MR Physics
• MR Techniques
• Artefacts
• Advanced Techniques
• Instrumentation
• MR Safety

147
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.

148
The Nobel Prize in Physiology or Medicine 2003
Paul C. Lauterbur
Sir Peter Mansfield
149

• 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.

150

• 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).

151

• 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.

152
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.

153
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.

154
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.

155
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.

156
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.

157
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.

158
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, ?0 ?B0.
• 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.

159
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.
160
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.

161
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 ).

162
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 MZ0. 
• 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 )

163

• 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.

164
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).

165
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).
166
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 magnetisati