Ultrasound Physics

Reflections &

Attenuation

‘97

Perpendicular Incidence

Sound beam travels perpendicular to boundary between two media 90o

IncidentAngle

1

2Boundarybetweenmedia

Oblique Incidence

Sound beam travel not perpendicular to boundary

ObliqueIncidentAngle

(not equal to 90o)

1

2

Boundarybetweenmedia

Perpendicular Incidence

What happens to sound at boundary?reflected

sound returns toward source

transmitted sound continues in

same direction

1

2

Perpendicular Incidence

Fraction of intensity reflected depends on acoustic impedances of two media

1

2

Acoustic Impedance =Density X Speed of Sound

Intensity Reflection Coefficient (IRC)&Intensity Transmission Coefficient (ITC)

IRCFraction of sound intensity

reflected at interface<1

ITCFraction of sound intensity

transmitted through interface<1

Medium 1

Medium 2IRC + ITC = 1

IRC Equation

Z1 is acoustic impedance of medium #1

Z2 is acoustic impedance of medium #2

2 reflected intensity z2 - z1

IRC = ------------------------ = ----------

incident intensity z2 + z1

For perpendicular incidence

Medium 1

Medium 2

Reflections

Impedances equal no reflection

Impedances similar little reflected

Impedances very different virtually all reflected

2 reflected intensity z2 - z1

Fraction Reflected = ------------------------ = ----------

incident intensity z2 + z1

Why Use Gel?

Acoustic Impedance of air & soft tissue very different

Without gel virtually no sound penetrates skin

2 reflected intensity z2 - z1

IRC = ------------------------ = ----------

incident intensity z2 + z1

Acoustic Impedance

(rayls)

Air 400Soft Tissue 1,630,000

Fraction Reflected: 0.9995

Rayleigh Scattering

redirection of sound in many directionscaused by rough surface with respect to

wavelength of sound

Diffuse Scattering & Rough Surfaces

heterogeneous mediacellular tissueparticle suspension

blood, for example

ScatteringOccurs if

boundary not smoothRoughness related to frequency

frequency changes wavelength higher frequency shortens wavelength shorter wavelength “roughens” surface

Specular Reflections

Un-scattered soundoccurs with smooth

boundariessimilar to light reflection

from mirroropposite of scatter from

rough surfacewall is example of rough

surface

Backscatter

sound scattered back in the direction of source

Backscatter Comments

Caused byrough surfacesheterogeneous media

Depends on scatterer’ssizeroughnessshapeorientation

Depends on sound frequencyaffects wavelength

Backscatter Intensity

normally << than specular reflections

angle dependancespecular reflection very angle dependentbackscatter not angle dependent

echo reception not dependent on incident angle

increasing frequency effectively roughens surfacehigher frequency results in more backscatter

PZT is Most Common Piezoelectric Material

Lead Zirconate TitanateAdvantages

Efficient More electrical energy transferred to sound & vice-

versaHigh natural resonance frequencyRepeatable characteristics

Stable designDisadvantages

High acoustic impedance Can cause poor acoustic coupling Requires matching layer to compensate

Resonant FrequencyFrequency of Highest Sustained

IntensityTransducer’s “preferred” or resonantresonant

frequencyExamples

Guitar StringBell

Operating Frequency

Determined bypropagation speed of transducer

material typically 4-6 mm/sec

thickness of element

prop. speed of element (mm /sec)oper. freq. (MHz) = ------------------------------------------------ 2 X thickness (mm)

Pulse Mode Ultrasoundtransducer driven by short voltage

pulsesshort sound pulses producedLike plucking guitar string

Pulse repetition frequency same as frequency of applied voltage pulsesdetermined by the instrument (scanner)

Pulse Duration Review

typically 2-3 cycles per pulseTransducer tends to continue ringing

minimized by dampeningdampening transducer element

Pulse Duration = Period X Cycles / Pulse

Damping MaterialGoal:

reduce cycles / pulseMethod:

dampen out vibrations after voltage pulse

Constructionmixture of powder & plastic or

epoxyattached to near face of

piezoelectric element (away from patient)

DampingMaterial

PiezoelectricElement

Disadvantages of Damping

reduces beam intensityproduces less pure frequency (tone)

Bandwidth

Damping shortens pulsesthe shorter the pulse, the higher the range

of frequencies Range of frequencies produced called

bandwidthbandwidth

Bandwidthrange of frequencies present in an

ultrasound pulse

Frequency

Intensity

Ideal

Frequency

Intensity

Actual

Bandwidth

OperatingFrequency

operating frequencyQuality Factor = ----------------------------- bandwidth

Quality Factor (“Q”)

UnitlessQuantitative Measure of

“Spectral Purity”

Frequency

Intensity

Actual

Bandwidth

Damping

More damping results inshorter pulsesmore frequencieshigher bandwidth lower quality factor lower intensity

Rule of thumb for short pulses (2 - 3 cycles)

quality factor ~ number of cycles per pulse

Transducer Matching LayerTransducer element has different acoustic

impedance than skinMatching layer reduces reflections at surface

of piezoelectric elementIncreases sound energy transmitted into body

Transducer – skin interface

Transducer Matching Layerplaced on face of transducerimpedance between that of

transducer & tissuereduces reflections at surface of

piezoelectric elementCreates several small transitions in acoustic

impedance rather than one large one

reflected intensity z2 - z1

IRC = ------------------------ = ----------

incident intensity z2 + z1

( )2 Matching

Layer

Transducer ArraysVirtually all commercial transducers

are arraysMultiple small elements in single

housingAllows sound beam to be electronically

FocusedSteeredShaped

Electronic Scanning

Transducer ArraysMultiple small transducersActivated in groups

Electrical ScanningPerformed with transducer arraysarrays

multiple elements inside transducer assembly arranged in either a line (linear array)

concentric circles (annular array)

Curvilinear Array Linear Array

Linear Array Scanning

Two techniques for activating groups of linear transducers Switched ArraysSwitched Arrays

activate all elements in group at same time Phased ArraysPhased Arrays

Activate group elements at slightly different times impose timing delays between activations of elements in

group

Linear Switched ArraysElements energized as

groupsgroup acts like one large

transducerGroups moved up & down

through elementssame effect as manually

translatingvery fast scanning possible

(several times per second) results in real time image

Linear Switched Arrays

Linear Phased ArrayGroups of elements energized

same as with switched arrays

voltage pulse applied to all elements of a group

BUTelements not all pulsed at

same time

1

2

Linear Phased Arraytiming variations allow beam

to be shapedsteeredfocused

Above arrows indicate timing variations.By activating bottom element first & top last, beam directed upward

Beam steered upward

Linear Phased Array

Above arrows indicate timing variations.By activating top element first & bottom last, beam directed downward

Beam steered downward

By changing timing variations between pulses, beam can be scanned from top to bottom

Linear Phased Array

Above arrows indicate timing variations.By activating top & bottom elements earlier than center ones, beam is focused

Beam is focused

Focus

Linear Phased ArrayFocus

Focal point can be moved toward or away from transducer by altering timing variations between outer elements & center

Linear Phased ArrayFocus

Multiple focal zones accomplished by changing timing variations between pulses•Multiple pulses required•slows frame rate

Listening ModeListening direction can be steered

& focused similarly to beam generationappropriate timing variations

applied to echoes received by various elements of a group

Dynamic Focusinglistening focus depth can be

changed electronically between pulses by applying timing variations as above

2

1.5 Transducer~3 elements in elevation directionAll 3 elements can be combined for thick slice1 element can be selected for thin slice

Elevation

Direction

1.5 & 2D TransducersMultiple elements in 2 directionsCan be steered & focused anywhere in 3D

volume