L14 Ultrasound(1)

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BME 340: Bioimaging

Lecture 14: Introduction to Ultrasound

Characteristics of ultrasound and its interactions with matter

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Ultrasound

Ultrasound imaging is the class of techniques that form images on thebasis of the reflection of sound waves from structure boundaries.

A pulse-echo acquisition (like radar).

Frequency range for medical imaging is 2-10 MHz.

An imaging modality that is genuinely wavelength limited with respect

to spatial resolution.

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Sound Propagation

Propagation of mechanical energy through a continuous

elastic medium bycompressionand subsequent expansionofthe medium itself.

As with EM radiation, wavelength is given as:

= c / f

with c typically given as m/s.

Sound velocity varies widely among materials and is a

function of the bulk modulus (B, a measure of elasticity and

resistance to compression) and thedensity() of the

medium:

Units are kg/(ms2) for B and kg/m3for .

Bc =

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Tissue Velocities

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Sound Propagation

Typical wavelengths in tissue:

f = 2MHz in soft tissue, = 0.77mm.

f = 10MHz is soft tissue, = 0.15mm.

f = 5MHz is soft tissue, = 0.31mm.

f = 5MHz in fat, = 0.29mm (5.8% from

soft tissue).

Wavelength determines the achievable spatial

resolution along the direction of the beam.

Higher frequency has a shorter wavelength.

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Sound Propagation

Penetrabilityof the sound energy varies with frequency.

In general, lower frequency beams will penetrate further.

Increasing frequency reduces penetrability.

For abdominal imaging, f = 3.5 5 MHz. For thyroid, breast, etc., f = 7.5 10 MHz.

Scanners generally supplied with a range of transducers to

cover several applications.

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Sound Propagation Theconstructiveanddeconstructive interference phenomena are very

important in shaping and steering the ultrasound beam.

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Pressure

Sound energy represents local variations inpressurewithin the propagating medium.

Pressure amplitude defined as the peak maximum or

minimum of the pressure waveform referenced to the

average value. SI unit is the Pascal (Pa) = 1 N/m2.

1 atmosphere = 100kPa.

Typical ultrasound beams in diagnostic imaging exceed 1

MPa in peak pressure.

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Intensity

Intensity is defined as thepower(energy/time) per unit area

and is proportional to the square ofpressure amplitude:

I P2

Typical unit is mW / cm2.

Intensity varies with peak pressure, and operating mode. Relative values expressed as dB:

Relative Intensity (dB) = 10 log (I2 / I1)

Relative Pressure (dB) = 20 log (P2 / P1)

Typical return echoes can be 60dB reduced in intensity over thetransmitted pulse.

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Example: Calculate the remaining intensity of a 100 mWultrasound pulse that loses 30 dB while traveling through

tissue.

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Ultrasound Interactions in Matter

A propagating sound wave can undergo reflection, refraction,

absorption, and scatter. Reflectionoccurs at boundaries where there is a difference in

acoustic impedance with the reflected energy traveling back

towards the source. This is the basis for image formation.

Refractionis the change in direction resulting from non-perpendicular incidence.

Scattering results from both reflection and refraction from small

structures and produces the characteristic background texture seen

in ultrasound images. Absorption is the conversion of sound energy to heat.

Attenuationis defined as the loss of intensity due to scatter and

absorption.

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Acoustic Impedance Acoustic impedance (Z) is defined as: Z = c

Where c is the speed of sound in m/s and is density in kg/m3.

The unit of Z is kg / (m2s), and is known as a rayl. Acoustic impedance

can be thought of as a measure of compressibility.

Sound waves will reflect from boundaries representing a mismatch in

acoustic impedance.

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Reflection and Refraction

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Reflection Reflection of sound energy from a boundary is a function of the

impedance mismatch at the boundary separating two materials:

Where RPis thereflection pressure coefficient, Prand Piare the

reflected and incident pressures respectively, Z1and Z2are theacoustic impedances.

The intensity reflection coefficient is given as:

Following conservation of energy, the transmitted intensity is

given as: TI= 1 RI

12

12

ZZ

ZZ

P

PR

i

r

P

+

==

2

12

12

+

== ZZ

ZZ

I

I

Ri

r

I

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Reflection

For perpendicular incidence on a boundary, the reflectedenergy returns to the transducer as an echo (time delay).

Where is much longer than structural variations in the

boundary, a smooth boundary is rendered (assumed in all

previous discussions). Reducing increases scatter off variations in the boundary

and a smaller return to the source.

For non-perpendicular incidence, reflection takes place at the

same angle away from the transducer resulting in loss ofsignal.

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Where c2>c1,total reflection can occur when the angle of incidence

is greater than the critical angle, defined as

Refraction This is the change in direction of transmitted sound energy upon a non-

perpendicular encounter with a boundary. Angles of incidence, reflection, and transmission are measured relative

to the normal to the boundary.

The index of refraction is determined by the difference in the speed of

sound across the boundary.

192

1

arcsin c

c

c =


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Scattering

Acoustic scattering results from objects on the order of a

wavelength in size (representing a rough surface).

Some organs have a characteristic surface structure that gives

rise to a characteristic scatter signature (useful diagnostically).

Rough reflectors reflect sound over a range of angles, thus

causing loss in amplitude of received echoes.

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Scattering Intensity of return signal from rough reflectors has less of a

dependence beam direction than that from smooth reflectors.

Along a rough boundary, differences in scatter amplitude show

up as differences in image intensity.

Factors determining echo amplitude:

Number of scatter structures/volume

Size of scatter structures

Boundary Z difference

Signal frequency

All else being the same, scatter increases with frequency. In US lingo, Hyperechoic= high scatter amplitude,

Hypoechoic= low scatter amplitude, relative to average

background signal, useful in characterizing anatomy.

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Attenuation

Attenuation results from loss of acoustic energy (converted to

heat) and scattering.

Attenuation coefficient () in units of dB/cm.

is approximately linear with frequency (i.e. doubling the

frequency doubles the attenuation).

General value for soft tissue is 0.5dB/cm/MHz.

Tissue half-value thickness (HVT) corresponds to thickness

for 3dB drop in intensity (or 6dB drop in pressure amplitude).

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Attenuation

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Attenuation

For medical imaging purposes, ultrasound detectors musthave a dynamic range on the order of 120-140dB in

pressure amplitude (factor of 107).

Deeper penetration requires lower frequencies.

Frequency dependence of transmission results in depth-dependent (low pass) filtering of broadband pulses.

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Attenuation

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Example: Calculate the approximate intensity HVT in soft

tissue for ultrasound beams of 2 and 10 MHz. Determine the

number of HVTs the incident beam and the echo travel at a 6-

cm depth.


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Review

What is the typical range of ultrasound frequency used formedical imaging?

Does longer wavelength imply better ultrasound penetrability?

The wavelength of a 2 MHz ultrasound beam is ________ mm

in soft tissue. (In soft tissue c = 1540 m/sec).

What is the constructive/deconstructive interference?

Calculate the remaining intensity of a 10 mW ultrasound pulse

that loses 60 dB while traveling through tissue.

What intensity fraction of an ultrasound beam is reflected from

an interface between two media with Z (acoustic impedance)values of 1.65 and 1.55?

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