basic physics of b-mode

7/29/2019 Basic Physics of B-mode

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Basic Physics of Nuclear

Medicine/Sonography & Nuclear Medicine

From Wikibooks, the open-content textbooks collection


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[edit] Sound Waves

Sound wavestravelling 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.

Theselongitudinal wavestravel with a velocity, v, of about 330 m/s in air at STP, and at highervelocities 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 hearyou scream', which was used to promote the movieAlien, is quite correct!

A sequence of compressions and rarefactions is referred to as one cycle, as illustrated. The

wavelength,, is defined as the length of one cycle and the frequency, f, as the number ofcycles which pass a fixed point every second. These quantities are related through the famous

equation:

v = f .

The human ear is sensitive to sound frequencies up to about 20 kHz, and waves of higher

frequency are referred to asultrasound. 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 forsmall, superficial objects.

Medium Velocity (m/s)

Air 331

Brain 1,541

Kidney 1,561

Liver 1,549
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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 avelocity 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. Thistechnique 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 interfacebetween 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 interfaceand 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:

Note that in this equation:

the average velocity of ultrasound in the tissue is used, and the factor, 2, 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:

Muscle 1,585

Fat 1,450

Soft Tissue (average) 1,540
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Illustration of the pulse-echo principle.

Ultrasound transducers exploit thepiezoelectric effectto cause a crystal to vibrate at ultrasoundfrequencies. The resultant vibrations generate pulses of compressions and rarefactions which

propogate 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 anultrasound pulse encounters a tissue interface.

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 producefurther echoes at other interfaces and a smallamount is absorbed. The reflectivity of an

interface depends on theacoustic impedanceof

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 forimaging purposes.

[edit] 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 ofultrasound 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

Interface Reflection Coefficient (%)

Soft Tissue - Air 99.9

Fat - Muscle 1.08

Fat - Kidney 0.64

Muscle - Liver 1.5
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amplified by a Receiver Amplifier whose output isdemodulatedbefore 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.

The Time-Gain Compensation (TGC) circuit provides for selective amplification of the echosignals 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 shownbelow:

Illustration of a linear array transducer interrogating different lines of tissue.
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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. Thelocations of echo-producing tissue interfaces are generally represented by bright pixels on a darkbackground, 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 phasedarray, 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.
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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 andforth during the scanning process, while the right panel illustrates a rotating arrangement of

single crystals:

Illustration of two designs of mechanical transducer.

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
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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 anLCD monitor. Prior to display, the image data can be post-processed usingan 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 inanother chapterof this wikibook. The box labelled P represents amicroprocessor which is used to control this scan conversion circuitry, as well as many otherfunctions 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:
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.

[edit] Doppler Ultrasound

TheDoppler Effectis widely exploited in the remote measurement of moving objects, and can beused 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 waveswhen 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.
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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, asillustrated 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, , towards a

blood vessel, which contains blood flowing with a velocity ofu m/s, at any instant. The

transducer emits ultrasound waves of frequency, fo, and echoes generated by moving reflectors in

the blood, e.g. red blood cells, have a frequency, fr. The difference between these twofrequencies, f, is related to the velocity of the flowing reflectors throught the following

equation:

where v is the velocity of sound in the medium.
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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. 0-15kHz. 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 ofthe distribution of blood velocities during a cardiac cycle by computing theirFourier transforms.

Its more common however to produce images of the distribution of frequency shifts within blood

vessels using techniques such as Colour-Flow orColour-Power imaging. These techniques areused 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 figureabove. A simplified block diagram of a sonography system used for such imaging is shown

below:

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