Lecture Physics

1842 – Christian Andreas Doppler

•Developed the early hypothesis of the Doppler Shift

•Frequency shift relative to motion

•Train whistle (relative to sound)

If a sound moves rapidly towards the observer

Audible frequency will increase

If a sound moves away rapidly

frequency will decrease

frequency will decrease

if moving toward you the pitch increases and once moving away from you it recedes

As red blood cells do not emit sound

we rely on the instruments to transmit sound through the tissue and to receive the echo from moving reflectors

the difference in the transmitted frequency and the reflected and changed frequency from moving blood is called

the Doppler shift

DOPPLER EFFECT Apparent change

in frequency of sound or light waves emitted by a source occurs as it moves away from or toward the observer.

DOPPLER EFFECT Sound that reflects

off a moving object undergoes a change in frequency.

DOPPLER EFFECT Objects moving toward the transducer

reflect sound at a higher frequency than that of the incident pulse; objects moving away reflect sound at a lower frequency.

Doppler imaging

The frequency of the reflected sound wave and is the same as the frequency transmitted only if the reflector is stationary

If the reflector is moving toward the transducer

the frequency of the echo will be higher than the transmitted frequency

If the reflector is moving away from the transducer

echo frequency will be lower than the transmitted frequency.

Two basic modes of transducer operation for medical diagnostic applications are

continuous wave and pulsed wave

Real-time instrumentation uses

only pulse-echo amplitude of returning echo to generate gray-scale information

Doppler instrumentation uses

both continuous and pulse-wave operations

Doppler shift is the difference between

receiving echo frequency and the frequency of the transmitted beam

This change in frequency of the reflected wave is caused by the relative motion between the reflector and the transducer’s beam

Doppler shift is usually only

a small fraction of the transmitted ultrasound frequency

Doppler shift frequency is proportional to

the velocity of moving the reflector or blood cell

Doppler effect produces a shift that is

the reflected frequency minus the transmitted frequency

When interrogating the same blood vessel with transducers of different frequencies

the higher frequency transducer will generate a larger Doppler shift frequency

Doppler angle

The angle that the reflector path makes with the ultrasound beam

As Doppler angle increases from 0 to 90 degrees

detected Doppler frequency shift decreases

At 90 degrees

the Doppler shift is zero, regardless of flow velocity

If the angle of the beam to the reflector exceeds 60 degrees

velocities will no longer be accurate.

The closer the Doppler angle is to zero

the more accurate the flow velocity

When a ceramic crystal is electronically stimulated

it deforms and vibrates and produces the sound pulses used in diagnostic sonography

The frequency of the transmitted signal depends on the size of thickness of the elements;

the small or thinner the elements, the higher the frequency

Frequency is expressed in Hertz

1 sound wave or cycle per second = 1 hertz

For diagnostic ultrasound, transmitted Doppler frequency is

between 2.0 –10 MHz

Sound is characterized according to its

Frequency

Frequency:

Describes the number of oscillations per second performed by particles of medium in which wave is propagating

1 oscillation/sec =

cycle/sec = 1 hertz (1 Hz)

1000 oscillations/sec =

1 kilocycle/sec = 1 kilohertz (1 kHz)

1,000,000 oscillations/sec =

1 megacycle/sec = 1 megahertz (1 MHz)

Velocity of propagation

Constant for given tissue

Not affected by the frequency or wavelength of pulse

in soft tissues, the assumed average propagation velocity is

1540 m/sec

Stiffness and density of the medium determine

how fast sound waves will travel through it

The more closely packed the molecules

the faster speed of sound

Velocity of sound differs greatly among

air, bone, and soft tissue

Sound waves travel slowly through

gas (air), at intermediate speed through liquids, and quickly through solids (metal)

Air-filled structures

impede sound transmission

Sound is attenuated through most

bony structures

Decibel (dB) unit

is used to measure the intensity (strength), amplitude, and power of an ultrasound wave

Using decibels allows sonographers to

compare the intensity or amplitude of two signals.

Power

The rate at which energy is transmitted

Power is the rate

of energy flow over the entire beam of sound and is often measured in watts (W) or milliwatts (mW)

Intensity

The power-per-unit area

Intensity is the rate

of energy flow across a defined area of beam and is measured in watts per square meter (W/m2) or milliwatts per square centimeter (mW/cm2).

Reflection

Occurs whenever the pulse encounters an interface between tissues with different acoustic impedances

Acoustic impedance

The measure of a material’s resistance to propagation of sound

Strength of reflection depends on the:

• Difference in acoustic impedance between tissues

•Interface size, surface characteristics, and orientation to the transmitted sound pulse

The greater the acoustic mismatch

the greater the backscatter, or reflection.

Specular reflectors

Large, smooth interfaces

When aligned perpendicular to the direction of the transmitted pulse

sound is reflected directly back to the active crystal elements in the transducer, and a strong signal is produced

When not oriented perpendicular to sound,

weaker signal is produced

Scattering

The redirection of sound in multiple directions, which produces a weak signal. This occurs when the pulse encounters a small acoustic interface or large interface that is rough (nonspecular reflector)

Refraction

Change in the direction of sound

Refraction occurs when sound encounters

the interface between two tissues that transmit sound at different speeds

(Refraction) Sound frequency remains constant

but the wavelength changes to accommodate the differences in the speed of sound

(Refraction) The result of this change in wavelength is

a redirection of the sound pulse as it passes through the interface

Absorption

The loss of sound energy, secondary to its conversion to thermal energy

Absorption is greater in

soft tissues than it is in fluid; i.e. is greater in bone than in soft tissues

Absorption is the major cause of

acoustic shadowing

Pulse duration

The amount of time the piezoelectric element vibrates after electrical stimulation

(Pulse duration) Each pulse consists of a band of frequencies called

bandwidth

Center frequency

• Produced by the transducer

• Resonant frequency of the crystal element

• Depends on the thickness of the crystal

Echoes that return to the transducer distort the crystal elements and

generate an electric pulse that is processed into the image

Higher-amplitude echoes produce greater crystal deformation and

generate larger electronic voltage, which is displayed as a brighter pixel

These two-dimensional images are known as B-mode or

brightness mode, images.

Resolution

of an imaging process distinguishes the adjacent structures in an object

• Important measure of image quality

• Determined by the size and configuration of transmitted sound pulse

(resolution) Always considered in three dimensions

axial, lateral, and azimuthal

Axial resolution

describes the ability to resolve objects that are located at different depths along the direction of the sound pulse within the imaging plane

Axial resolution depends on the

direction of the sound pulse, which, in turn, depends on the wavelength

Higher frequency probes produce

shorter pulses and better axial resolution but with less penetration

Lateral resolution

The ability to resolve objects within the imaging plane located side by side at the same depth from the transducer

• Can be varied by adjusting the focal zone of transducer (point at which the beam is narrowest)

Beam width determines

lateral resolution

If two reflectors are closer together than the diameter or width of the transducer

they will not be resolved

Azimuthal (elevation) resolution:

The ability to resolve objects the same distance from the transducer but located perpendicular to the plane of imaging

Azimuthal resolution is also related to

the thickness of the tomographic slice

Slice thickness

is usually determined by the shape of crystal elements or characteristics of fixed acoustic lenses

Attenuation

The reduction in intensity and amplitude of a sound wave as it travels through a medium as some of energy absorbed, reflected, or scattered

• The sum of acoustic energy losses

In human soft tissue, sound attenuates at a rate of

0.5 dB/cm per million hertz

If air or bone is coupled with soft tissue

attenuation increases

Attenuation through a solid calcium interface such as a gallstone produces

a shadow with sharp borders on the image

Differences in acoustic impedance in biologic tissues are generally so slight that

only a small component of the ultrasound beam is reflected at each interface

• Exception is air-tissue and bone interfaces.

Anatomy beyond the lung and bowel

cannot be imaged because of air interference

Bone conducts sound at a

significantly faster speed than soft tissue

Real-time compound imaging allows

sound to be steered at multiple angles, including perpendicular to the body to produce the best image

Harmonics

are components whose frequencies are integral multiples of the lowest frequency (the “fundamental” or “first harmonic”)

Harmonic imaging involves

transmitting at frequency f and receiving at frequency 2f (the second harmonic)

(Harmonic Imaging) Filtering out fundamental frequency and creating images from echoes of the second harmonic should result in

an image relatively free of noise formed during the passage of sound through distorting layers of the body wall

Linear-Array Transducer

Activates a limited group of adjacent elements to generate each pulse

(Linear-Array Transducer) Pulses travel in the same direction (parallel) and are oriented perpendicular to the transducer surface.

Results in rectangular image

Linear-Array Transducer resolution

High resolution in the near field

Curved-Array Transducer

Uses a linear-array transducer with surface of transducer re-formed into a curved convex shape.

• Produces a moderately sized, sector-shaped image with a convex apex.

(Curved-Array Transducer) resolution

Wider far field of view; slightly reduced resolution

(Curved-Array Transducer) use

Probe can be formatted for many different applications with varying frequencies for use in abdomen to smaller endoluminal scanning.

Pulsed Wave Doppler

Waves sent and received by the same crystal in the transducer

(Pulsed Wave Doppler) Two types

Spectral and Color Doppler

Transmitter

supplies electrical signals to the transducer for producing a sound beam