high school physics day april 3 rd, 2013 ultrasound physics & instrumentation

High School Physics DayApril 3rd, 2013

Ultrasound Physics & Instrumentation

Pegasus Lectures, Inc.COPYRIGHT 2006

“SPI in a Nutshell”Disclaimer:

This is an overview of some important concepts in ultrasound medical imaging intended for high school physics students. It is intended to spark student interest in physics and the myriad of applications of physics, including medical ultrasound. This is not a complete introduction to medical ultrasound – there are many important topics not mentioned due to time constraints. Some slides are based on Pegasus Lectures, copyrighted material.

“SPI in a Nutshell” Outline

Basic Physics Overview

Wave physics

Transducers

Piezoelectric crystals

Instrumentation Overview

From pulses to images

Attenuation and Some Example of Imaging Artifacts

Signal-to-noise ratio

Doppler and Hemodynamics

Bioeffects

Mechanical and thermal indexes


Metric AbbreviationsThink about how much easier the metric system is than the English system; all you have to do is move the decimal point by the number of places specified by the exponent.

G = 109 1,000,000,000M = 106 1,000,000k = 103 1,000h = 102 100da = 101 10d = 10-1 0.1c = 10-2 0.01m = 10-3 0.001 = 10-6 0.000001n = 10-9 0.000000001


Distance Equation

We will begin by calculating the time it takes for sound to travel 1 cm in the body (assuming a propagation velocity of 1540 m/sec). Since we want to solve for time, we must rewrite the equation in the form time = distance/rate.

So it takes 6.5 sec to travel 1 cm or:13 sec to image a structure at 1 cm because of the roundtrip effect.

26

distancetime

rate1 cm 1 10 m

so time = 6.5 10 sec 6.5 secm m

1540 1540sec sec

Distance rate time


Distance Equation

Time Distance Imaging Depth

6.5 sec 1 cm 0.5 cm

13 sec 2 cm 1 cm

26 sec 4 cm 2 cm

39 sec 6 cm 3 cm

52 sec 8 cm 4 cm

65 sec 10 cm 5 cm

78 sec 12 cm 6 cm

91 sec 14 cm 7 cm

104 sec 16 cm 8 cm

117 sec 18 cm 9 cm

130 sec 20 cm 10 cm

0 cm

1 cm

6.5 sec

6.5

sec


Time of Flight in the Body

Fig. 3: Imaging 1 cm Requires 13 sec (Pg 39)


Addition of Waves

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0

0.25 0.5

0.75 1

Time (sec)

Am

plitu

de

-1

-0.75

-0.5

-0.25

0

0.25

0.5

0.75

1

0

0.25 0.5

0.75 1

Time (sec)

Am

plitu

de Sum = 0

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0

0.25 0.5

0.75 1

Time (sec)

Am

plitu

deConstructive Interference

Destructive Interference

Partial Constructive Interference


Wave Propagation ClassificationMechanical waves are further classified according to how they propagate.

Fig. 2: (Pg 84)


Transverse Wave Propagation

Fig. 3: Transverse Waves (Pg 85)

Transverse waves propagate by particle motion that is perpendicular or “transverse” to the wave propagation direction.


Longitudinal Wave Propagation

Fig. 4: (Pg 85)

Longitudinal waves propagate by particle compression and rarefaction that results in particle motion that is “along” or in the same direction as the wave propagation direction.


Wave CharacteristicsAs sound propagates, it causes mechanical changes in the medium

Frequency :

Propagation Speed :

Wavelength :

Amplitude :

1f Hz = and Period ( T : sec )

sec

c ( m/sec )

( meters )

A ( Volts, or any units for acoustic variable

s )


Graphical Depiction of a 2 Hz wave

Fig. 10: (Pg 93)


Wavelength EquationThe wavelength of a sound wave depends on both the frequency and the propagation speed.

A higher propagation speed “stretches” out the wave.

A lower frequency “stretches” out the wave.


Propagation Velocity (c)In Level 1, we discussed the fact that sound was determined strictly by the properties of the medium. It is now important to discuss which properties of the medium affect the propagation velocity and how.

The propagation velocity is related to the square root of the bulk modulus of the medium.

The propagation velocity is inversely related to the density of the medium.

modulusc


Propagation Velocities in the Body

Table 5: (Pg 121)

Medium Propagation Velocity

Air (25 degrees C) 347 m/sec

Lung 500 m/sec

Fat 1440 m/sec

Water (25 degrees C) 1495 m/sec

Brain 1510 m/sec

“Soft Tissue” Average 1540 m/sec

Liver 1560 m/sec

Kidney 1560 m/sec

Blood 1560 m/sec

Muscle 1570 m/sec

Bone 4080 m/sec


Fig. 17: (Pg 606)

Speed Error Artifact ExampleThis speed error case results from a needle entering into a cystic structure. The needle appears bent giving rise to the name “broken needle” or “bayonet” sign.


Relationship of intensity with Amplitude

2AmplitudePower

Intensityarea area

So if the amplitude is doubled, the power increases by a factor of four, resulting in an increase in intensity by a factor of four.

Recall that voltage is a measure of amplitude.


Same Frequency – Different Amplitude

Fig. 33: (Pg 135)


AttenuationAttenuation is a measure of how the medium affects the wave.

Attenuation will be divided into three subtopics:

Absorption

Reflection

Refraction


Reflection – Acoustic ImpedanceThe amount of reflection from a boundary is determined by the acoustic impedance mismatch.

What this equation says is: the greater the acoustic impedance mismatch between mediums, the greater the amount of reflection.

How much reflection would there be if z2 = z1?


TransmissionAll of the energy at an interface between media must be conserved.

Excluding absorption, this means that whatever energy does not reflect must transmit (continue on through the patient).

Can you imagine why it is so important to not have too much reflection from any one interface?


Refraction and Snell’s Law

θincident

θtransmitted

θreflected

cincident

ctransmittedMedium 2

Medium 1


Range Specificity and a Very Short Pulse

Fig. 2: (Pg 194)

Notice that the echoes from each of the three mountains return at distinct times such that each mountain is resolved (range resolution).


Foundational PW Drawing Revisited

Fig. 25: (Pg 220)


Scanned Modalities (Animation)

(Pg 207 A)


Creating a Frame & Acoustic LinesEach transmit burst or “pulse” represents the beginning of one acoustic line. Multiple acoustic lines constitute one frame (or an image).

Time

Transmit 1 Transmit 2 Transmit 3


Ultrasound transducers use the piezoelectric effect to convert electrical energy into mechanical energy and mechanical energy back into electrical energy.

Piezoelectric Effect

PZ

TP

ZT

Electrical to acoustic transformation

Acoustic to electrical transformation


Piezoelectric Effect

Fig. 2a Expansion Fig. 2b Contraction Fig. 2c At Rest

(Pg 235)


Lateral Resolution and Beamwidth

Fig. 14: (Pg 248)

Lateral Resolution Beamwidth

The lateral resolution equals the lateral beamwidth dimension. If the beam is wider than the distance between two structures, the echo from both structures will overlap, making it impossible to distinguish between the two structures laterally.


SNR (can ask SBI students about it)

(Pg 307)

307 A: Poor SNR 307 B: Good SNR 307 C: Poor Apparent SNR

307 D: Poor Apparent SNR 307 E: Good SNR 307 F: Poor Apparent SNR


Relative Motion and AngleNotice that Observer A sees the opposite effect of Observer B. Observer B sees a compression in the wavelength (a higher frequency) whereas Observer A sees an elongated wavelength, (a lower frequency). The higher frequency is referred to as a positive shift, whereas the lower frequency is referred to as a negative shift.

Fig. 6: (Pg 532)


Fast Moving Plane (Animation)

(Pg 522)


Doppler EquationIn Level 1, we expressed the Doppler equation in a simplified form, ignoring the angular correction of the cosine term. We can now add the angular correction of the cosine term as follows:

2 cosoDop

f vf

c

Where:

( )

cos

= (

Dopf Doppler shifted frequency relative to transmit frequency

v velocity of the sound source (target)

angle correction

insonification angle or ang

)

c

le to flow

speed of sound


Determining Flow Direction

Fig. 54: (Pg 576)

Notice in this example that the flow is not changing in direction or speed (constant velocity) yet the flow looks very different traversing the vessel. This appearance is the result of the changing angle to flow formed between the constant flow direction and the varying steering angle.


Flow Direction: Case 3 (Animation)

(Pg 580 C)

Pegasus Lectures, Inc.

Assuming no loss of energy to heat, as the flow accelerates, there is a decrease in potential energy and a compensatory increase in kinetic energy (transitioning from region 1 to region 2) As the velocity decreases (region 2 to region 3) the kinetic energy decreases and the potential energy increases back to the same level as in region 1.

Flow Conversion between Potential and Kinetic Energy

Fig. 1: (Pg 742)

PE

KE PE

KE

PE

KE

Region 1Lower Velocity

Region 2Higher Velocity

Region 3Lower Velocity

Pegasus Lectures, Inc.

Bioeffects Intensity Restrictions

“Highest Risk of Thermal”

“Lowest Risk of Thermal”

“Lowest Risk of Mechanical”

“Greatest Risk of Mechanical” B-Mode

PW

PW(larger gate)

CW


Basic System Functions

Fig. 6: (Pg 308)

American Registry of Diagnostic Medical Sonographers (ARDMS)

• Must be registered sonographer (ARDMS or CCI) to practice in Florida

• CCI exams easier than ARDMS

• Two principal prerequisites to take ARDMS board exams:

• Passing grade in ultrasound physics course http://www.ardms.org/credentials_examinations/

• Clinical experience (several months, duration depends on specific exam) http://www.ardms.org/files/downloads/Prerequisite_Chart.pdf

Thank you!

• Questions?• If not, take your worksheet and follow SBI students to ultrasound lab• You can find this presentation at my website:

http://www.nhn.ou.edu/~blandon/click on “SBI High School Physics Day”

high school physics day april 3 rd, 2013 ultrasound physics & instrumentation

Documents

form time

time of flight

time constraints

time secamplitudesum

transverse waves pg

wave propagation direction

transverse wave propagationfig

medical ultrasound