# Basic Physics of Nuclear Medicine/Sonography & Nuclear Medicine

!A sonographic study of valves in a patient\'s
heart.

This is a developing chapter of a wikibook entitled Basic Physics of
Nuclear Medicine.

Sonography is an application of the SONAR
principle in medical imaging where the surfaces of internal organs and
their inner structure can be depicted (see the image below). This
imaging modality has the advantage of not using ionizing radiation and
is frequently used to provide correlative anatomical information for
nuclear medicine images. An overview of basic features of sonographic
imaging is provided in this chapter.

We\'ll start with a consideration of relevant characteristics of sound
waves before describing various imaging methods.

## Sound Waves

Sound waves travelling through air consist of
periodic fluctuations in air pressure, called compressions and
rarefactions, as illustrated below:

!Illustration of a vibrating tuning fork producing a sequence of
compressions and rarefactions in the surrounding
air.

These longitudinal waves travel with
a velocity, *v*, of about 330 m/s in air at STP, and at higher
velocities in denser media, such as water and soft tissue. Indeed a
medium is needed for the waves to propagate -- remember that the physics
behind the statement \'In space no one can hear you scream\', which was
used to promote the movie Alien "wikilink"), is quite
correct!

A sequence of compressions and rarefactions is referred to as one
**cycle**, as illustrated. The **wavelength**, *λ*, is defined as the
length of one cycle and the **frequency**, *f*, as the number of cycles
which pass a fixed point every second. These quantities are related
through the famous equation:

```{=html}
<div class="center">
```
*v* = *f* λ

```{=html}
</div>
```
The human ear is sensitive to sound frequencies up to about 20 kHz, and
waves of higher frequency are referred to as
ultrasound. Much higher frequencies are used
in diagnostic sonography, in the
range 1-15 MHz. Low frequencies in this range can be used to image large
deep structures, while high frequencies can be used for small,
superficial objects.

  Medium                      Velocity (m/s)
  --------------------------- ----------------
  **Air**                     331
  **Brain**                   1,541
  **Kidney**                  1,561
  **Liver**                   1,549
  **Muscle**                  1,585
  **Fat**                     1,450
  **Soft Tissue (average)**   1,540

The velocity of ultrasound waves is identical to that of sound waves in
the same medium, and is given in the following table for a range of
internal organs. Note that a velocity of 1,540 m/s is generally assumed
for soft tissue in sonographic imaging and represents an *average* of
that for a number of tissues, muscles and organs.

Ultrasound waves are generally produced in pulses for sonographic
imaging, with the time interval between pulses used to detect ultrasound
echoes produced within the body. This technique exploits what\'s known
as the **Pulse-Echo Principle**, as illustrated in the diagram below.
The upper half of the diagram depicts an ultrasound transducer emitting
one pulse of ultrasound into a hypothetical body, which is assumed to
consist of just two tissues. The lower half of the diagram depicts the
situation after the ultrasound pulse has encountered the interface
between the two tissues. A reflected pulse is shown travelling back
towards the transducer, i.e. the echo, and a transmitted pulse is seen
to continue into the second tissue.

The length of time taken for the pulse, once produced by the transducer,
to travel to the interface and the echoed pulse to return is termed the
**pulse-echo time**, *t*, and its measurement allows the depth, *d*, of
the interface to be determined using the following equation:

```{=html}
<div class="center">
```
$d = \frac{\overline{v}t}{2}$

```{=html}
</div>
```
Note that in this equation:

:\*the average velocity of ultrasound in the tissue is used, and

:\*the factor, `<span style="color:red;">`{=html}2`</span>`{=html},
arises because the pulse and its echo must travel the same distance, one
from the transducer to the interface and the other from the interface
back to the transducer:

!Illustration of the pulse-echo
principle.{width="256"}

Ultrasound transducers exploit the piezoelectric
effect to cause a crystal to vibrate
at ultrasound frequencies. The resultant vibrations generate pulses of
compressions and rarefactions which propagate through the tissues.
Echoes produced by tissue interfaces are then detected by the same
crystal -- exploiting the piezoelectric effect once again.

The ultrasound pulse becomes attenuated as it passes through tissue and
four phenomena result when it encounters a tissue interface, as
illustrated below:

!Illustration of phenomena which result when an ultrasound pulse
encounters a tissue
interface.{width="256"}

  Interface                Reflection Coefficient (%)
  ------------------------ ----------------------------
  **Soft Tissue -- Air**   99.9
  **Fat -- Muscle**        1.08
  **Fat -- Kidney**        0.64
  **Muscle -- Liver**      1.5

Some of the energy in the pulse is scattered through a process called
**non-specular reflection**, some of it generates an echo in a
**specular reflection** process, some of it is transmitted through the
interface to produce further echoes at other interfaces and a small
amount is absorbed. The reflectivity of an interface depends on the
acoustic impedance of the two tissues
involved, and representative values are shown in the table.

Notice in the table that a huge reflection can occur at a soft tissue --
air interface. Its for this reason that a coupling medium is used
between the transducer and the patient\'s skin. Internal reflections are
seen in the table to be of the order of 1%, yielding a useful
transparency for imaging purposes. 

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## Ultrasound Scanner

A simplified block diagram of a sonography system is shown in the figure
below. The type of scanner shown operates using a linear array
transducer, which we\'ll learn more about shortly. We can see the
**Master Timer** in the top right of the figure. This circuit sets the
number of ultrasound pulses which the transducer generates every second
-- a factor referred to as the Pulse Repetition Frequency (**PRF**). Its
also seen that echo pulses picked up by the transducer are amplified by
a **Receiver Amplifier** whose output is
demodulated before being fed to a **Scan
Converter** so that the location and amplitude of detected echoes can be
displayed.

!Simplied block diagram of an ultrasound scanner which uses a linear
array
transducer.{width="256"}

The Time-Gain Compensation (**TGC**) circuit provides for selective
amplification of the echo signals so as to compensate for attenuation of
distant ultrasound echoes and suppress more proximal ones. The switch
array is used to excite the multiple crystals in the transducer as shown
below:

!Illustration of a linear array transducer interrogating different
lines of
tissue.{width="256"}

!B-mode image from a patient\'s liver
scan.

In the simplest arrangement, each crystal generates an ultrasound pulse
one after the other so that sequential lines of tissue can be rapidly
and continuously insonated.

The ultrasound image is referred to as a **B-Mode** scan and consists of
a 2D representation of the echo pattern in a cross-section of tissue
with the transducer position at the top of the image. The locations of
echo-producing tissue interfaces are generally represented by bright
pixels on a dark background, with the amplitude of each echo signal
being represented by the pixel value -- see the image on the right.

The image shown was actually acquired using a more sophisticated
transducer called a **phased array**, which generates a sector-shaped
scan. This type of transducer also uses a linear array of small
crystals, but with them excited in complex timing sequences, controlled
by delay circuitry -- as shown in the figure below. The ultrasound beam
can be steered to scan a region in this manner while being focussed at
different depths simultaneously.

!Illustration of a phased array
transducer.

There are numerous other transducer designs, each of which have
particular advantages in different clinical applications. Two designs of
mechanical transducer are shown below as examples. The left panel
illustrates a transducer with a single crystal which is rocked back and
forth during the scanning process, while the right panel illustrates a
rotating arrangement of single crystals:

!Illustration of two designs of mechanical
transducer.{width="512"}

Components of the scan conversion circuitry are illustrated in the
following figure:

!Simplified block diagram of the scan converter of an ultrasound
scanner.

The figure illustrates the process of digitizing the analogue echo
signals using an analogue-to-digital converter (**ADC**) and applying
pre-processing to the digital data using an input look-up table
(**ILUT**) prior to storage in random access memory. This memory is
filled in the sequence which was used to scan the patient and read out
in a manner suitable for the display device, which is typically an LCD
monitor. Prior to display, the image data can
be post-processed using an output look-up table (**OLUT**) so that
contrast enhancement and other processing functions can be applied. Note
that we\'ve encountered this type of digital image processing in a more
general form in another
chapter
of this wikibook. The box labelled
`<span style="color:blue;">`{=html}`<b>`{=html}μP`</b>`{=html}`</span>`{=html}
represents a microprocessor which is used to control this scan
conversion circuitry, as well as many other functions of the scanner,
e.g. the timing used for phased array emission and reception.

A digital image resolution widely used in sonography is 512 x 512 x
8-bits -- a magnified view of the central region of the liver scan shown
earlier is provided below to illustrate the digital nature of the data:

!Magnified view of the central region of the liver scan shown
earlier.

We conclude this section with photos of a sonography system and typical
transducers:

!`<span style="color:white;">`{=html}.`</span>`{=html}

#top

## Doppler Ultrasound

The Doppler Effect is widely exploited in
the remote measurement of moving objects, and can be used in medical
sonography to generate images (and sounds!) of flowing blood. The effect
is demonstrated by all wave-like phenomena, be they longitudinal or
transverse waves, and has been used with light, for instance, to reveal
that we live in an expanding universe! Its also exploited using radio
waves in highway speed traps, and can be experienced with sound waves
when an ambulance passes by with its siren blaring.

Let\'s take the example of a train engine sounding its whistle, as
illustrated in the diagram below:

!Illustration of the origin of the Doppler
Effect.

When the train is stationary, and there isn\'t a wind blowing, the sound
will emanate equally from the whistle in all directions, as illustrated
on the left. When the train is moving, however, sound frequencies will
be increased in the forward direction and reduced in the opposite
direction, as illustrated on the right, to an extent dependent on the
velocity of the train. This apparent change in frequency of the sound
waves experienced by a stationary listener is referred to as the Doppler
Shift.

The situation for exploiting the Doppler Effect for the detection of
blood flow is illustrated in the following diagram:

!Illustration of blood flow detection using the Doppler Effect with
ultrasound
waves.

The diagram shows a Doppler transducer placed on the skin and aimed at
an angle, θ, towards a blood vessel, which contains blood flowing with a
velocity of *u* m/s, at any instant. The transducer emits ultrasound
waves of frequency, *f*~o~, and echoes generated by moving reflectors in
the blood, e.g. red blood cells, have a frequency, *f*~r~. The
difference between these two frequencies, Δ*f*, is related to the
velocity of the flowing reflectors through the following equation:

```{=html}
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```
$\Delta f = f_0 - f = \frac{2f_0 u \cos \theta}{v}$

```{=html}
</div>
```
where *v* is the velocity of sound in the medium.

So, for instance, when ultrasound with a frequency in the range 2-10 MHz
is applied in medicine to detect blood flowing in arteries (where
typical velocities are 0-5 m/s), the equation above reveals that the
frequency differences will be in the audible range of sound frequencies,
i.e. 0-15 kHz. Their signals can therefore be fed through speakers so
that this sound can be heard.

Its also possible to examine the frequency content of Doppler shifts to
examine subtle details of the distribution of blood velocities during a
cardiac cycle by computing their Fourier
transforms.
Its more common however to produce images of the distribution of
frequency shifts within blood vessels using techniques such as
**Colour-Flow** or **Colour-Power** imaging. These techniques are used
to automatically fuse Doppler signals with B-Mode ultrasound images, as
illustrated below:

!A colour-flow image on the left with a colour-power image on the
right.

Colour-flow processing is sensitive to the direction of blood flow, i.e.
it can detect both positive and negative Doppler shifts, and uses a
colour look-up table
(CLUT)
so that shifts in one direction are displayed in shades of red with
those in the other direction in shades of blue -- as illustrated by a
patient\'s jugular vein and carotid artery depicted in the left panel of
the figure above. A simplified block diagram of a sonography system used
for such imaging is shown below:

!Block diagram of a colour-flow sonography imaging
system.

The system uses a beam former circuit to excite the crystals of the
phased array transducer for B-Mode imaging and Doppler shift detection
in a rapid alternating manner, with the echo signals being fed to B-Mode
scanning circuitry and the Doppler signals fed to an autocorrelation
detector for analysis. Output
data from these circuits are then blended within the scan conversion and
formatting circuitry, prior to display of the fused image.

As a final point, note that the colour-power image displayed above does
not contain any blood-flow direction information, since this technique
computes the power of reflected Doppler-shifted pulses instead of their
frequency content.

#top

