Medical Ultrasound

1
Medical Ultrasound

• Spring 2008

2
Chapter 6. Ultrasound Imaging System
3
Diagnostic Radiology

• X-Ray Images
• High resolution lt 0.1 mm
• Most used in the world

4
Diagnostic Radiology

• Fluoroscope Images
• Continuously capturing images
• Monitoring of surgery

5
Diagnostic Radiology

• CT Images
• 2D/3D
• High resolution 1mm

6
Ultrasound Imaging

• Safest of all
• OBGYN
• Low resolution 5 mm1mm
• fast imaging for heart imaging
• Cardiovascular imaging
• Doppler imaging blood perfusion
• .

7
MRI

• MRI (Magnetic Resonance Imaging)
• Proton Magnetization
• 3D image
• Excellent in Soft Tissue Contrast
• Safer than CT
• Resolution 1 mm range
• fMRI functional, physiological imaging
• .

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Medical Ultrasound Systems
9
Medical Ultrasound Systems

• There are three major ultrasound system makers
  GE, Siemens, Philips
• Those big threes are actually the big three of
  medical imaging systems.
• GE is especially strong in MRI
• Siemens has strong edge on Ultrasound Imaging
• Current issue in ultrasound imaging systems is
  high quality and small portable systems.

10
System Structure

• Pulser

Limiter
Preamp
Transducer
Bandpass Filter
CPU
Display
TGC
Scan Conversion
Envelope Detector
Beam Forming
11
CPU

• CPU main functions
• Reorganization of transducer types
• Control from user
• Output to pulser
• Display adjustment
• Frame rate, Region of interest,
• Beam forming schematics
• Storage of data
• Transfer data
• Now a days, high power DSP processors are added
  for the fast post-process.

12
Pulser

• Pulser sending high voltage electrical signal to
  transducer
• Ultrasound transducer is a voltage driven
  component. Hence high voltage range of 80160
  voltage is required for general ultrasound
  imaging system. Power consumption is still low.
• In order to achieve this goal, switching type
  power amplifier is adapted.
• .

As can be seen in the left side figure, the
output is simple push-pull MOSFET switch. The
driver is controlled from CPU directly with
digital signal. In order to switch the MOSFET
fast enough (over 10 MHz) gate voltage is
generally over 1215V
out
13
Pulser

• We do not expect students understand the details
  of circuit. But the output need to be studied a
  bit carefully.
• The output from the MOSFET switching is square
  wave at best.
• Then what is the output from the transducer we
  wish to obtain?
• Enveloped sine wave
• Then how can we obtain a sine wave
• from square wave?
• .

14
Pulser

• If you understand FT well enough, it is not that
  difficult to understand.
• Lets consider a Fourier Transform of single
  square pulse whose pulse duration is short
  compared to the systems natural frequency.
• .

15
Pulser

• As shown in the previous slide, the FT of square
  wave is sinc function in frequency domain.
• Now lets assume that the pulse duration is so
  short that it almost appears to be impulse to the
  system. It is possible if we think of sinc
  function and time duration T. If T gets smaller
  the sinc function becomes wider.
• The matter is if the T is short enough compared
  to the systems frequency characterisitics.
• .

16
Pulser

• Hence, we can easily think by applying a single
  short enough pulse, the system would assume that
  it get a impulse input.
• Impulse means flat frequency components which
  means all the frequency components is fed to the
  system.
• Since a transducer is a high Q-factor system, it
  has a relatively narrow bandwidth (compared to
  general communication system). Hence, only the
  frequency component related to the pass band will
  be translated to the acoustic field.
• Here is the beauty of MOSFET switching power
  amplifier. It does not need to make a sinusoidal
  wave for analog output. It simply need to make
  large enough a square pulse which automatically
  turned to be sinusoidal wave

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Pulser

• But we have to be very careful about a couple of
  things.
• If you use too high Q-material then, rising
  (ringing) time is too long so that the pulse
  becomes too long.
• Think of PZT4 and PZT5
• Ideally, impulse input means higher amplitude for
  shorter pulse. So that same energy will be
  transferred.
• However, the amplitude of the MOSFET switch is
  fixed (there is small number of choice but it is
  limited), so that a shorter pulse means smaller
  energy.
• Since there is no system in nature can create
  energy (energy is just transformed form one to
  another), we cannot reduce the pulse length
  infinitely.

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Transducer

• .

• We already covered the main part of transducer.
• But that is not enough to understand all the
  aspect of transducers used in medical ultrasound
  system.
• Especially, we need to consider array
  transducers.
• But we will start from the beginning again in
  this chapter.
• Lets assume we have a line transducer length of
  L at the center of coordinate system.
• .

z
?
x
L/2
-L/2
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Transducer

• .

• Almost the same as the previous example but
  slightly different.
• Then, the aperture function will be represented
  as follows
• .

a(x)
1
x
L/2
-L/2
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Transducer

• .

• You could say, wait a minute, it is different
  with the previous example. But it isnt in
  reality.
• In the previous example, we counted all the
  factors, but we only care about angular dependent
  factors. So keep this in mind.
• And it is called directivity of a transducer.
• .

21
Transducer

• Therefore, directivity is simple Fourier
  Transform of aperture function.
• Of course we have to change the variable from f
  to sin?/?
• And it is called directivity of a transducer.
• .

• .

L
3/L
1/L
2/L
-1/L
-2/L
sin?/?
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Transducer

• Lets change the figure a bit.
• Please keep in mind it is function sin ? not ?
• First lobe at the center main lobe, the others
  are side lobes
• .

• .

L
3 ?/L
?/L
2 ?/L
- ?/L
-2 ?/L
sin?
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Array Transducer

• .

• Lets go a bit more realistic.
• None of the ultrasound imaging machine utilizes
  single element transducer currently. We are using
  array transducer.
• Array can be simplified as follows graphically.
  sample points
• .

z
?
x
L/2
-L/2
d
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Array Transducer

• .

• Mathematically aperture function will be changed
  as follows
• .

z
?
x
L/2
-L/2
d
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Array Transducer

• .

• The graphically the directivity can be shown as
  follows
• Please, keep in mind we are not in frequency
  domain. We are in the space domain.
• We have learned main lobe and side lobes. Then
  what is this replica of whole sinc function. It
  is called grating lobes.

L/d
sin?
- ?/d
?/d
2 ?/d
0
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Array Transducer

• .

• Now lets go more realistically.
• There is no point array transducer as we have
  assumed. Every single element has finites size.
• So the transducer is can be represented
  graphically as follows.
• .

z
?
w
x
L/2
-L/2
d
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Array Transducer

• .

• Then aperture function can be as follows
• Hence, the aperture function is train of rect
  functions.
• This is physically reasonable. Even though we try
  our best to reduce or increase the size of
  element, the gap cannot be zero and width cannot
  be longer than distance between element.
• dgtw always.

a(x)
x
L/2
-L/2
d
w
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Array Transducer

• .

• Lets find a directivity of this array model
• It appears a bit confusing at first glance, but
  if you follow the steps it is not so difficult.
  It can be represented as a convolution of rect
  function to sample train at the limited zone.
• .

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Array Transducer

• .

• Not it is time to see the graphical
  representation.
• .

D(?)
Lw/d
-?/d
-?/w
sin(?)
?/d
?/w
?/L
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Array Transducer

• .

• Now it is clear there is additional sinc function
  which envelope the original directivity.
• As we already notified the wltd, this imply a very
  important aspect of array transducer.
• Lets ask ourselves, what would be the better
  transducer wd or wltltd?
• We want an imaging transducer which can focus a
  very small zone, so that we can have better
  resolution. But there is something called grating
  lobe in array which send/receive signal from
  where we do not want to see.
• Hence, we need to reduce grating lobe. From the
  graphical representation, wd grating lobe will
  be close to zero.

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Array Transducer

• .

• There is additional aspect we should not ignore.
• As we have seen in the graph, directivity is
  function of sin(?). Which implies directivity is
  meaningful only (-1,1) unless we consider complex
  number.
• Additionally, directivity is frequency dependent.
  Where is frequency related part? ? is wavelength
  so that ? c/f.
• This indicates that high frequency will has
  smaller main lobe with same aperture size. Hence
  high frequency transducer will have better
  angular (lateral resolution).
• And if the aperture size becomes larger, then the
  resolution will be higher.

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Array Transducer

• .

• There are additional aspects we cannot ignore.
• As we have seen in the graph, directivity is
  function of sin(?). Which implies directivity is
  meaningful only (-1,1) unless we consider complex
  number.
• Additionally, directivity is frequency dependent.
  Where is frequency related part? ? is wavelength
  so that ? c/f.
• This indicates that high frequency will has
  smaller main lobe with same aperture size. Hence
  high frequency transducer will have better
  angular (lateral resolution).
• And if the aperture size becomes larger, then the
  resolution will be higher.

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Array Transducer

• .

• Then here is a question for you. Why do we not
  use large enough transducer at high enough
  frequency?
• First, even though we want to increase frequency,
  it is mainly limited by attenuation. As we
  already studied attenuation is proportional to
  frequency in soft tissue. We can improve it by
  stronger pulse, but there is safety issue
• Second, the array element distance is order of
  wave length. It indicates the distance is order
  of 100um. If we want to make an array 30cm, it
  should have a lot of elements. It is not simply a
  matter of array element. Individual elements are
  accompanied with electronics. That is a lot.
  Also it is not handy.
• There is additional aspect with this issue.
  Acoustic window is some times limit us. Ex) the
  cardiac imaging case
• Frequency is 210MHz and the size is 110 cm

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Beam-width

• Since we have understand directivity of a beam,
  it is time to calculate the beam width more
  precisely.
• We know that we are only interested in the main
  lobe. We will assume that a good engineer already
  took care of grating lobe at this point.
• The beam width is defined in terms of the
  isocontour lines as can be seen below figure.
• Generally the criterion is half maximum
  criterion.
• .

z
?
??
x
L/2
-L/2
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Beam-width

• In order to calculate the beam width, we have to
  look into the directivity function again.
• .

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Beam-width

• From the equation obtained in the previous slide,
  we have to decide condition where D(???) is ½
  compared to D(?). That is not so convenient, so
  we will do that only at ? 0
• Wait a minute it is not right. Where did we do
  wrong? The only half of the beam width. So it
  should be corrected as follow
• .

37
Beam-width

• Lets go a bit more generally. If we do not
  limit ourselves to the zero angular position,
  then it beamwidth will be as follows
• What is this means?
• Imagine two beam located closely together. If we
  assume that two beams from two separate points.
  We want to distinguish that signal source. That
  is the definition of resolution. If we think of
  rough summation, they should be far enough that
  the half of maximum value of main lobe is not
  overlapped. That is called Full Width Half
  Maximum criterion.

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Directivity of Transmit Receive

• So far we have covered the directivity of
  transmission
• Is that enough for ultrasound imaging system?
• No. Ultrasound imaging is utilizing the
  transmitting and receiving. In other word, the
  transducer transmit a sound wave and wait for a
  while to receive the reflected signal.
• Then what is the directivity of receiving part?
• Fortunately we do not need to go through the all
  the steps again. Since, transmitting and
  receiving has identical directivity.
• Hence overall directivity of transmit and
  receiving system is

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Beam steering

• So far we have studied the directivity
  intensively.
• We have now understand the beam directivity and
  beam width of array transducer.
• Now it is time to ask ourselves, what we would do
  to look at the other angular position?
• Easiest answer is rotation the transducer so that
  the main lobe of beam look at the wanted angular
  position.
• This is 1st generation 2D ultrasound imaging
• But that is not good enough, it is inconvenient.
• The answer is driving each transducer elements
  with a certain way, so that it works as if the
  transducer is rotated. That is called beam
  steering.

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Beam steering
z
?

• Lets assume we want to see the angular position
  of ?. As can bee seen above figure, we can give
  delays to pulses from individual element. This
  effectively rotate the transducer. Hence we can
  see different angular position without actually
  moving or rotating the transducer.

x
L/2
-L/2
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Beam Steering
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Beam Focus

• If you have paid attention to the beam
  directivity very carefully, we might have noticed
  that beam directivity is spreading as distance
  increasing.
• It is natural law. Lets imaging a polar
  coordinate system. If ?? is fixed, then the
  actual length between two points separated that
  much is proportional to the distant from the
  origin.
• However, it is not like that in medical
  ultrasound imaging. The following figures will
  show the difference.

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Beam Focus
44
Beam Focus

• Why is this happening? We have calculated the
  directivity from mathematical formula? How could
  this be different?
• This answer is simple. It is because the model
  is wrong. We know that we have to simplify the
  model in order to make the integral can be
  solvable. In the mean while we find that we
  adapted Fraunhoffer Approximation which is
  basically assuming the wave is not circular wave
  but plane wave.
• However, it is reasonable only when the distance
  between the transducer and the point of measure
  is far compared to transducer size and frequency.
  But medical ultrasound does not fit to that
  regime from the beginning. Hence it is
  reasonable to is not like that in medical
  ultrasound imaging.
• The details of beam focusing at a certain
  distance from the transducer is beyond the scope
  of our work.

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Limiter

• Lets look back slide 11. There is something
  called limiter.
• What is limiter is function?
• Limiter is protection circuit to bypass the high
  voltage driving pulse.
• As we have seen from the schematic, the
  transducer is transmitter and receiver at the
  same time.
• We also learned that the pulse is high voltage
  range of 100 Vpp
• But receiving circuit is generally A/D converter
  range of 1 Vpp or less. This means that receiving
  circuit needs some sort of protection. It is
  achieved by pass circuit.
• .

A/D
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Preamplifier / Band pass filter

• Almost all the electrical system has preamplifier
  (analog).
• Generally, preamp is also works as band pass
  filter.
• Hence, preamp is amplifying the signal around 100
  dB in ultrasound imaging system in addition, it
  also filtering out all the unnecessary frequency
  components. In most of cases, the filter has Q
  factor around 1 (Center frequency/band width).
• For example, if the system is adapting 5 MHz
  transducer, then its bandwidth is 2.5MHz to
  7.5MHz. Of course it is generally not ideal
  filter, since it is implemented with hardware.