The Physics of Ultrasound Eei

Extended Response Task

2

Year 12 Physics

Miss Meni

Semester 4, Term 3

Due Date: 19th August

2011

3

Table of Contents

1.0 Introduction:.......................................................................3

2.0 History of the technology:....................................................3

3.0 Analysis of technology design and function:..........................6

3.1 Wave Propagation:................................................................................7

3.2 Piezoelectric Transducer:......................................................................8

3.2.1 Electrostriction................................................................................9

3.2.2 The Piezoelectric Effect.................................................................11

3.3 Attenuation:........................................................................................11

3.4 Acoustic Impedance:...........................................................................13

4.0 Comparison to alternatives:................................................15

5.0 Future developments:........................................................17

6.0 Conclusion:........................................................................19

7.0 References:.......................................................................20

8.0 Appendices:.......................................................................22

8.1 Appendix 1:.........................................................................................22

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The Physics of Ultrasound

1.0 Introduction:

Medical imaging is the technique used by doctors to create internal

images of the human body for clinical reasons such as examining and

diagnosing diseases (NDT Resource Centre, 2011). The aim of medical

imaging is to deliver an image of inside the body in a way that is as non-

invasive as possible (Radiological Society of North America, 2011).

This report will investigate ultrasound as a form of medical imaging and

determine the history of the technology, comparison to alternative forms

of imaging, future developments and will investigate the physics behind

ultrasound in all regards.

2.0 History of the technology:

Prior to modern day ultrasonic testing, numerous physics concepts had to

be first discovered. The following is a timeline of physics discoveries that

lead to the common use of ultrasound imaging (see figure 1).

500BC

The greek philosopher and mathematician Pythagoras experimented with the vibration of strings.This is the earliest study of sound and was the beginning of the idea that sound travels in waves.

400BC

Another greek philospher, Aristotle, suggested that the movement of air carries sound.This again contributed to to the modern day use of ultrasound as this theory explains the movement of sound waves.

150AD

Leonardo DaVinci discovered and proved that sound travels in waves.This proved Aristotles theory and again contributed to the idea of ultrasound.

Figure 1: Timeline of Ultrasound

5

1640

Marin Merenne first measured the speed of sound through air.

1660

Robert Boyle discovered that that sound waves require a medium to propagate.

1665-

1669

Sir Isaac Newton formulated a relationship between the speed of sound in a medium and the density and compressiblity of a medium.

Mid 1700's

Daniel Bernoulli explained that a string can vibrate at more than one frequency.

1790

Lazzaro Spallanzani experimented with bats and discovered that they flew through the air using hearing rather than sight.This lead to the theory that sounds waves can be reflected or echoed back to the original source. This is still the basis of all ultrasound testing.

1826

The swiss physicist/engineer Jean-daniel Colladon discovered sonography with an underwater bell. With this, he accurately determined the speed of sound through water.

1881

Pierre Curie found a connection between between electrical voltage and pressure on a crystalline material, I.e. The piezoelectric effect.This was the biggest breakthough in the history of ultrasound since the discovery of sound waves as it is the basis behind the modern day piezoelectric transducer.

1912-

1915

After the sinking of the titanic, Paul Langevin invented the first hydrophone to detect icebergs. This was the first transducer; a device that could send and receive low frequency sound waves. This was another major step foward in the history of ultrasound.

Late

1930's

The Austrian psychiatrist Dr. Karl Dussik was the first to use ultrasound pictures in an attempt to diagnose brain tumors.The procedure was called "hyperphonography" and he used heat sensitive paper to record the echos.This is considered the first the first use of ultrasound for medical purposes.

Continued next

page.

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Late 1940's

Dr. George Luwig was the first to record the difference in sound waves as they travelled through tissues, organs, muscles and gallstones.This once again was an extravigant contribution to the history of ultrasound.

1950's

Scottish professor Ian Donald invented the B mode scanner.

1960's

Douglas Howry and Joseph Holmes impoved the B-mode scanner by inventing a tranducer that came into direct contact with the patient. Before this, patients had to be submerged in water.This was the start of ultrasound as we know it today.

1970 -

present

Dr. John Wild and John Reid improved various ultrasound equipment such as the B-mode instrument that could swing side to side and image patients from different angles. This instrument was used to to detect breast tumors.They also invented an A-mode scanner for the detction of ovarian cancer.

(Genesis Ultrasound, 2010. Simmons, n.d).

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3.0 Analysis of technology design and function:

Ultrasound is form of mechanical sound energy that travels through the

body in order to produce an internal image (Ultrasound for Regional

Anesthesia, 2008). Ultrasound is used in medicine for the purpose of

examining and diagnosing a variety of issues within the human body. This

form of medical imaging helps physicians to assess symptoms such as

pain, swelling and infections in many of the body’s internal organs such as

the heart, liver, gallbladder, spleen, pancreas, brain, kidneys and most

commonly it is used for examining an unborn child (fetus) in pregnant

patients (Radiological Society of North America, 2011).

Several functional units are required for a typical ultrasound inspection

system. These functional units include: a pulsar/receiver, a transducer and

display services. The pulsar/receiver is an electronic device that produces

high voltage electrical pulses. Driven by the pulsar, the transducer

generates high frequency ultrasonic energy, which in turn produces sound

energy that propagates through materials in the form of longitudinal

sound waves (NDT Resource Centre, 2011). When a defect (e.g. A crack) is

in the wave path, part of the energy is reflected back to the transducer

from the surface of the flaw (see figure 2). The transducer then converts

the reflected wave signal back to an electrical signal and the result is

displayed on a screen (NDT Resource Centre, 2011).

Figure 2: Generation of Ultrasound

(NDT Resource Centre, 2011)

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3.1 Wave Propagation:

Sound travels as a longitudinal, mechanical wave. Sound waves are

capable of traveling through any medium (e.g. Body tissue), however

without a medium, sound does not exist. The medium itself is in fact

motionless, however, the individual atoms and molecules in the medium

oscillate about their equilibrium position and interact with the

neighbouring molecules, thus transferring energy (The Physics Classroom,

n.d). These waves exist as a disparity of pressure. An area of increased

pressure on a sound wave is called a compression, whereas a region of

decreased pressure on a sound wave is called a rarefaction (Media

College, n.d)(see figure 3).

The speed of sound is the rate of the transmission of energy along a chain

of particles. It depends solely on the medium it is traveling through.

Predominantly, the elastic and inertial properties have the greatest affect

on the velocity of the wave (The Physics Classroom, n.d). With relation to

ultrasound, the speed of sound fluctuates for different biological mediums;

however, the accepted average for the speed of sound through soft tissue

is 1540 m/s (Radiological Society of North America, 2011). The speed of

sound can be found for different soft body tissues using:

Figure 3: Sound Wave

(Ultrasound for Regional Anethesia, 2008)

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V=√CρWhere: v is the speed of sound.

C is the elastic constant

p is the material density.

Due to the elastic and inertial properties of the various soft body tissue,

the speed of ultrasound travels slowest through mediums such as air and

the lung and fastest through bone (see figure 5).

3.2 Piezoelectric Transducer:

A piezoelectric transducer is an instrument used for the conversion of

electrical energy into mechanical vibrations (NDT Resource Centre, 2011).

They rely on two phenomena known as electrostriction and the

piezoelectric effect. Piezoelectric ceramic is used as the active element of

all transducers and their function is to create ultrasound waves at a

frequency in excess of 20,000 Hz (Radiological Society of North America,

2011).

Figure 4: Speed of Sound Equation

Figure 5: Speed of Ultrasound Waves through different

Biological mediums


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3.2.1 Electrostriction

The crystals used in piezoelectric transducers are polarized (i.e. some

parts of the molecule are positively charged, while other parts of the

molecule are negatively charged) with electrodes attached to two of its

opposite faces (NDT Resource Centre, 2011) (see figure 6). Thus, when in

the presence of an electric field, the polarized molecules will align

themselves with the electric field (see figure 7). This alignment of

molecules causes the piezoelectric crystal to change its dimensions; this is

the phenomenon known as electrostriction (NDT Resource Centre, 2011)

(see figure 8).

(Genesis Ultrasound, 2010)

Figure 7: Alignment of Molecules in Electric Field

Figure 6: Piezoelectric Transducer


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(No Author, 2007)

Thus, the piezoelectric crystal changing dimensions (i.e. expanding and

contracting) due to electrostriction leads to the production of an

ultrasound wave. The repetition of this process leads to the formation of

an ultrasound beam. An ultrasound beam is generated in pulses and each

pulse consists of approximately 2 or 3 series of the same frequency

(Radiological Society of North America, 2011) (see figure 9).


The distance travelled per pulse is known as the “pulse length” (see figure

9). The shorter the wave pulse, the better the axial resolution of the final

ultrasound image (Radiological Society of North America, 2011).

The Pulse Repetition Frequency (PRF) is the rate of pulses emitted by the

transducer (Radiological Society of North America, 2011) (see figure 9).

Figure 9: Ultrasound Beam

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3.2.2 The Piezoelectric Effect

Some materials, when subjected to mechanical stress, are able to produce

electricity (Hyperphysics, n.d). This phenomenon is called the piezoelectric

effect. It occurs in ultrasound when the balance of charged molecules

inside the piezoelectric crystal is disturbed (Radiological Society of North

America, 2011) (see figure 10).

(Stevens Institute of Technology, 2007)

3.3 Attenuation:

The further the ultrasound wave traverses the body and as the depth of

penetration is increased, the amplitude of the original beam is attenuated.

Thus, the energy that is lost in ultrasonic testing is known as attenuation

(NDT Resource Centre, 2011). Attenuation is due to three things:

Absorption

Reflection

Scattering of the beam

The most common of the three is absorption, which counts for 80% of all

attenuation in ultrasonic testing (Radiological Society of North America,

2011). Absorption takes the acoustic energy and transfers it into heat

production (Ultrasound for Regional Anethesia, 2008).

Figure 10: Piezoelectric Effect

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The unit of measurement for attenuation is decibels per centimeter of

tissue. This figure is represented by the attenuation coefficient of the

specific tissue type (see figure 11).


As the attenuation coefficient is increased, the energy lost of the original

sound beam is also increased; therefore this follows a proportional

relationship. This is why bone, which has a very high attenuation

coefficient, limits beam transmission to such a high degree. The frequency

and distance of the ultrasound beam also has an effect on the total

attenuation (Ultrasound for Regional Anethesia, 2008) (see figure 12).

Figure 11: Attenuation Coefficients of various body tissues

Figure 12: Graph of the Effect that the Frequency has on

Attenuation

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By observing the above graph it can be seen that as the frequency of the

ultrasound beam is increased, so does the attenuation. Therefore, the

frequency is directly proportional to the attenuation of an ultrasound

beam (NDT Resource Centre, 2011).

Although the majority of attenuation is due to absorption, approximately

20% of this energy loss is due to reflection and scattering. The amount of

reflection is established by the variance in acoustic impedances of the two

tissues at the boundaries (Ultrasound for Regional Anethesia, 2008).

3.4 Acoustic Impedance:

Acoustic impedance is the resistance of a tissue to the passage of

ultrasound (Ultrasound for Regional Anethesia, 2008). Acoustic impedance

can be found using a simple equation (see figure 13).

z=pv

Where: z is the acoustic impedance

p is the density of the medium

v is the propagation velocity of ultrasound through the medium.


A large difference in acoustic impedance between mediums is called

“acoustic impedance mismatch”. The greater the acoustic mismatch the

greater the percentage of ultrasound reflected and less transmitted (NDT

Resource Centre, 2011).

There is a variation of acoustic impedance with different body tissues (see

figure 14).

Figure 13: Acoustic Impedance Formula


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Analysing this table shows that the strongest reflected ultrasound beams

would be for air as it has very small acoustic impedance when compared

to other body tissues. Bone would also have a high degree of reflection as

it has an acoustic impedance that is very high relative to other body

tissues (Ultrasound For Regional Anethesia, 2008).

The reflection co-efficient can be modeled and calculated by the following

equation (see figure 12).

R=(Z2−Z1Z2+Z1 )2

Where: R is the reflected wave

Z1 is the initial impedance

Z2 is the final impedance

Figure 14: Variation of Acoustic Impedance with Body Tissues

Figure 12: Reflection Co-efficient


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For example, the reflection between muscle and bone is 41%, meaning

41% of the beam is reflected when the wave travels from muscle through

to bone (see appendix 1).

The table also demonstrates why it is necessary for a gel to be applied to

the patient when an ultrasound test is in progress. The gel acts as an

“acoustic coupling medium” on the transducer and its purpose is to

eliminate any air pockets between the transducer and the skin surface.

Without this gel, 99.9% of the ultrasound beams will be reflected away,

therefore only 0.01% the beam will be available to penetrate body tissue

and produce an image (see appendix 1) (Ultrasound for Regional

Anethesia, 2008).

4.0 Comparison to alternatives:

Ultrasound imaging yields many benefits, however it also carries some

disadvantages (see figure 15).

Figure 15: Advantages and Disadvantages of Ultrasound

Advantages Disadvantages

Very easy to perform an ultrasound

test.

The resolution of images is quite

often restricted.

Examinations are non-invasive. The

body does not have to be cut open

and nothing has to be inserted

inside the body.

The reflection of sound waves when

passing from tissue to gas has an

effect that limits ultrasound from

being used in areas containing gas,

such as the lungs.

Examinations are quick, convenient

and relatively inexpensive.

Due to attenuation, ultrasound does

not pass well through bone,

therefore images of the brain can

be taken but will often be distorted.

Does not use ionizing radiation,

therefore no harmful effects can

come from these examinations.

Extremely good at examining soft

tissue such as the eye, heart and

other internal organs.

Provides real-time imaging,

therefore it can be a good tool for

procedures such as needle biopsies.

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As ultrasound testing examines such a diverse range of problems within

the body, it can be used as an alternative to most other forms of medical

imaging. Due to this fact, there is no other form of medical imaging that

uses similar technology to ultrasound. However, as an example,

ultrasound can image the brain and so can MRI, therefore the comparison

will be made between ultrasound and MRI in order to determine the most

effective method of imaging the brain.

Magnetic Resonance imaging, or MRI, is another form of non-invasive

medical imaging that is used to evaluate and diagnose problems with

internal organs (Radiological Society of North America, 2010). MRI uses a

very powerful magnetic field and radio frequency pulses in order to

generate an image of the brain (Radiological Society of North America,

Figure 16: Advantages and Disadvantages of MRI

Advantages Disadvantages

Examinations are non-invasive. Due to the powerful magnetic field,

patients with pacemakers and other

cannot undergo a MRI procedure.

Patients are not subjected to

ionizing radiation.

Cannot always distinguish between

malignant tumors and benign

diseases.

Enables the detection of problems

they may be behind bone without

any distortion of the image.

A small number of risks and side

effects are present.

Enables the detection of

abnormalities of the brain, as well

as the assessment of the normal

functional anatomy of the brain.

Patients can become claustrophobic

in the small area inside the MRI

machine.

Larger patients may not fit inside

the MRI machine.

Examinations can take up to 4

hours; during the time patients are

required to stay motionless.

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2010). Like ultrasound, MRI carries many advantages and disadvantages

(see figure 16).

By analysing figures 15 and 16 it can be seen that both ultrasound and

Magnetic Resonance Imaging yield many benefits. Both forms of imaging

do not require any ionizing radiation as ultrasound uses sound waves to

image the patients, whilst MRI uses radio waves that redirect the axis of

spinning protons in a powerful magnetic field (Radiological Society of

North America, 2010). In addition, neither forms of imaging are invasive,

however both are effective at imaging soft tissue such as the brain. Due to

this, and the fact that both forms of imaging are non-invasive to the

patient, it can be said that both ultrasound and MRI are effective forms of

brain imaging (Simmons, n.d).

However, due to the large attenuation of the ultrasound wave when

passing through bone (the skull), the final image can be distorted,

whereas magnetic resonance imaging passes through bone, leaving a

high-resolution image. It is due to this that magnetic resonance imaging is

the most effective way of non-invasively imaging the brain.

5.0 Future developments:

Ultrasound is a rapidly developing form of medical imaging and has come

a long way since it began in the late 1930’s. Originally, all ultrasound

pictures produced were two-dimensional images. The 1980’s saw the

introduction of three-dimensional images that works in the same way as

2D, however the transducer is moved in a circular motion over the organ,

tissue or fetus to be imaged and pictures are taken from multiple angles

and planes. This renders the surface of the organ or fetus and a sculpture

like image is created (Genesis Ultrasound, 2010).

Future developments in ultrasound are beginning to emerge now in the

form of four-dimensional Doppler ultrasound. Unlike 2D and 3D ultrasound,

4D ultrasound uses several pictures in rapid succession that gives the

effect of motion. This effect is achieved by the phenomenon of the Doppler

effect. The transducer detects movement inside the body by the

19

frequency of the returned echoes. A high frequency that is received

means the object is moving closer to the transducer and lower frequencies

mean the object is moving away. The images received are immediately

displayed on the display screen is such quick succession that the

movements inside the body can be seen in real-time (Genesis Ultrasound,

2010).

Even more advanced from 4D imaging is hologram ultrasound. Hologram

ultrasound allows the ultrasound beam to pass completely through the

object it is imaging whilst a second wave is transmitted simultaneously in

order to create a 3D hologram (see figure 17).

(Genesis Ultrasound, 2010)

The resulting hologram images would be capable of displaying images in

great finer detail than currently possible with ultrasound and even MRI

scans. For example, currently ultrasound cannot detect calcification, which

Figure 17: Holographic Ultrasound

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is an early marker of breast cancer, however hologram ultrasound would

provide images with such fine detail as the sound waves are passing

completely through the tissue or organ, there would be no ‘clouding’ of

the image (Genesis Ultrasound, 2010). Therefore with the introduction of

hologram ultrasound in the near future, the number of patients killed by

breast cancer every year could be drastically reduced due to the early

detection that this form of ultrasound could provide. Additionally,

cardiovascular disease could also be detected much earlier using this form

of ultrasound as the image would provide clear pictures of inside various

parts of the heart, including the pulmonary veins, left and right ventricle

and the

left and

right

atriums (see figure 18).

Figure 18: Diagram of a Heart

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The detail that holographic ultrasound images produce could in fact lead

to the detection of heart-valve disease or hardening of the arteries in such

early stages that is not at the moment possible (Genesis Ultrasound,

2010). Once again, this could significantly reduce the amount of patients

who die from preventable diseases such as these cardiovascular

infections.

6.0 Conclusion:

The aim of this report was to investigate ultrasound as a form of medical

imaging. It was found that the history of ultrasound dates back to 500BC

when Pythagoras experimented with sound and its properties. It was also

found that ultrasound is a very effective way of imaging the body non-

invasively, using mechanical sound waves produced from piezoelectric

crystals expanding and contracting due to electrostriction and the

piezoelectric effect. When compared to Magnetic Resonance Imaging,

ultrasound proved to be the less efficient way of imaging the brain

because of the distortion of the ultrasound image due to the attenuation

that the bone in the skull produces. Lastly, it was found that hologram

ultrasound is a future development that would have positive effects on

diagnosing breast cancer when it comes into use in the near future.

7.0 References:

B.A.T.S Research Group. (2011). Physics of Ultrasound. Retrieved July 10,

2011, from Better Anethetics Through Sonography (BATS):

http://www.bats.ac.nz/resources/physics.php

22

Genesis Ultrasound. (2010). 4D Ultrasound uses the Doppler effect to

show motion. Retrieved August 1, 2011, from Genesis Ultrasound:

http://www.genesis-ultrasound.com/4D-ultrasound.html

Genesis Ultrasound. (2010). A Condenced History of Ultrasound. Retrieved

August 1, 2011, from Genesis-Ultrasound: http://www.genesis-

ultrasound.com/history-of-ultrasound.html

Genesis Ultrasound. (2010). Hologram Ultrasound. Retrieved August 2,

2011, from Genesis Ultrasound: http://www.genesis-

ultrasound.com/Hologram-Ultrasound.html

Hyperphysics. (n.d). Piezoelectric Effect. Retrieved July 16, 2011, from

Hyperphysics:

http://hyperphysics.phy-astr.gsu.edu/hbase/solids/piezo.html

Media College. (n.d). How Sound Waves Work. Retrieved June 26, 2011,

from Media College: http://www.mediacollege.com/audio/01/sound-

waves.html

NDT Resource Centre. (2011). Acoustic Impedance. Retrieved June 23,

2011, from NDT Resource Centre:

http://www.ndt-ed.org/EducationResources/CommunityCollege/Ultra

sonics/Physics/acousticimpedance.htm

NDT Resource Centre. (2011). Attenuation of Sound waves. Retrieved July

23, 2011, from NDT Resource Centre:


sonics/Physics/attenuation.htm

NDT Resource Centre. (2011). Basic Principles of Ultrasound Testing.

Retrieved June 23, 2011, from NDT Resource Centre:


sonics/Introduction/description.htm

23

NDT Resource Centre. (2011). Characteristics of Piezoelectric Transducers.

Retrieved June 27, 2011, from NDT Resource Centre:


sonics/EquipmentTrans/characteristicspt.htm

No Author. (2007). Introduction: The Piezoelectric Effect. Retrieved August

1, 2011, from Piezoelectric Materials:

http://www.piezomaterials.com/

Physics 247. (n.d). Physics tutorial: Ultrasound Physics. Retrieved June 29,

2011, from Physics 247: http://www.physics247.com/physics-

tutorial/ultrasound-physics.shtml

Radiological Society of North America. (2011). General Ultrasound

Imaging. Retrieved June 26, 2011, from Radiology Info:

http://www.radiologyinfo.org/en/info.cfm?pg=genus

Radiological Society of North America. (2010). MRI of the Body. Retrieved

August 2, 2011, from Radiology Info:

http://www.radiologyinfo.org/en/info.cfm?pg=bodymr

Simmons, A. (n.d). Medical Physics - Ultrasound. Retrieved June 29, 2011,

from Genesis:

http://www.genesis.net.au/~ajs/projects/medical_physics/ultrasound

/index.html

Stevens Institute of Technology. (2007). Piezoelectric Energy Harvesting.

Retrieved August 3, 2011, from 07-08 Senior Design: Group 3:

http://www.ece.stevens-tech.edu/sd/archive/07F-08S/websites/grp3/

piezoelectric.html

The Physics Classroom. (n.d). Sound Properties and Their Pereption.

Retrieved June 26, 2011, from The Physics Classroom:

http://www.physicsclassroom.com/class/sound/u11l2c.cfm

24

Ultrasound for Regional Anethesia. (2008). Basic Principles. Retrieved June

25, 2011, from Ultrasound for Regional Anethesia:

http://www.usra.ca/basic_p

8.0 Appendices:

8.1 Appendix 1:

Calculations for Reflection:

R = ?

Z1 = 1.71 (see figure 14)


R=(Z2−Z1Z2+Z1 )2

¿( 1.71−7.81.71+7.8 )2

¿0.41

R%=R×100

¿0.41×100

¿41%

R = ?

Z1 = 0.0004 (see figure 14)


R=(Z2−Z1Z2+Z1 )2

¿( 0.0004−1.650.0004+1.65 )2

¿0.999

R%=R×100

¿0.999×100

25

¿99.9%

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The Physics of Ultrasound Eei