Outline• What is ultrasound• Ultrasonic signal generation• Diagnostic Ultrasound

– Ultrasound imaging– Array systems, Co-Arrays, K-space– Beamformers– Biosensors

• Theraupatic Ultrasound– Effect of US->Heating, vibrating,etc.– US power transmission and the applications

• Doppler effect and the applications• Microfluidics applications

What is Ultrasonic wave?

• Wave, a wave is a disturbance or oscillation that travels through space and matter, accompanied by a transfer of energy. Wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium.

• There are two main types of waves:– Mechanical Waves: Propagate through a medium, and the

substance of this medium is deformed.– Electromagnetic Waves: do not require a medium. Instead,

they consist of periodic oscillations of electrical and magnetic fields generated by charged particles

Mechanical Waves• Longitudinal Wave: wave particles vibrate

back and forth along the path that the wave travels.

• Compressions: The close together part of the wave

• Rarefactions: The spread-out parts of a wave

Mechanical Waves

• Transverse Wave: wave particles vibrate in an up-and-down motion.

• Crests: Highest part of a wave• Troughs: The low points of the wave

Wave Properties

• In liquids and gases, US propagates as longitudinal waves.

• In solids, US propagates also as transversal waves.

• Amplitude: is the maximum distance the particles in a wave vibrate from their rest positions.

• Frequency : the number of waves produced in a given time

Wave Properties

Frequency= #ofwaves/time

• Wavelength: The length of a single wave.• #ofwaves = (Total displacement in a given

time) / (The length of a single wave)• => Frequency = Total

displacement/wavelength*Time)• Wave Velocity - is the speed with which a wave crest

passes by a particular point in space. (wave velocity=Total displacement/time). It is measured in meters/second.

• Result: Wave Velocity = Frequency Wavelength

Speed of Sound

• Medium velocity m/secair (20 C) 343air (0 C) 331water (25 C) 1493sea water 1533diamond 12000iron 5130copper 3560

glass 5640

Speed of Sound Waves

Bv

Y… Young’s modulus

B… Bulk modulus of medium

…density of material

Bulk modules determines the volume change of an object due to an applied pressure P.

ii VVP

VVAFB

///

strain volumestress volume

Yv

In gas and liquids: In solids:

iLLAFY

//

strain tensilestress tensile

Young’s modules determines the length change of an object due to an applied force F.

Ultrasound

- sound waves with frequencies above the normal human range of hearing. Sounds in the range from 20-100kHz

Infrasound - sounds with frequencies below the normal human range of hearing.Sounds in the 20-200 Hz range

Types of US Waves

• Bulk Waves: 3 Dimensional propagation• Guided waves: Propagates at surfaces,

interfaces and edges. (Surface Acoustic Waves). Reigleigh wave. Lowe Wave Shear Horizontal Wave etc.

Interference• the result of two or more sound• waves overlapping

Diffraction

• No-one has ever been able to define the difference between interference and diffraction satisfactorily. It is just a question of usage, and there is no specific, important physical difference between them.

Richard Feynman

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Interactions of US with Tissue Reflection (smooth homogeneous interfaces of size

greater than beam width, e.g. organ outlines)

Rayleigh Scatter (small reflector sizes, e.g. blood cells, dominates in non-homogeneous media)

Refraction (away from normal from less dense to denser medium, note opposite to light, sometimes produces distortion)

Absorption (sound to heat)– absorption increases with f, note opposite to X-rays– absorption high in lungs, less in bone, least in soft

tissue, again note opposite to x-rays

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Acoustic parameters of medium: • Interaction of US with medium – reflection and back-

scattering, refraction, attenuation (scattering and absorption)

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Acoustic parameters of medium

Speed of US c depends on elasticity and density r of the medium: K - modulus of compressionin water and soft tissues c = 1500 - 1600 m.s-1, in bone about 3600 m.s-1

1. smKc

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Attenuation of US expresses decrease of wave amplitude along its trajectory. It depends on frequency

Ix = Io e-2ax a = a´.f2

Ix – final intensity, Io – initial intensity, 2x – medium layer thickness (reflected wave travels „to and fro“), a - linear attenuation coefficient (increases with frequency).Since

a = log10(I0/IX)/2x

we can express a in units dB/cm. At 1 MHz: muscle 1.2, liver 0.5, brain 0.9, connective tissue 2.5, bone 8.0

Acoustic parameters of medium

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Acoustic parameters of medium

Attenuation of ultrasound When expressing intensity of ultrasound in decibels, i.e. as a logarithm of Ix/I0, we can see the amplitudes of echoes to decrease linearly.

xkIIx

IIe

II xxxx ,

00

2

0

log2ln aa

depth [cm]

I or P[dB] attenuation

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Acoustic impedance: product of US speed c and medium density

Z = . c (Pa.s/m)

Z.10-6: muscles 1.7, liver 1.65 brain 1.56, bone 6.1, water 1.48

Acoustic parameters of medium

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We suppose perpendicular incidence of US on an interface between two media with different Z - a portion of waves will pass through and a portion will be reflected (the larger the difference in Z, the higher reflection).

Acoustic parameters of medium: US reflection and transmission on interfaces

P1 Z 2 - Z 1

R = ------- = --------------- P Z2 + Z1

P2 2 Z 1

D = ------- = --------------- P Z2 + Z1

Coefficient of reflection R – ratio of acoustic pressures of reflected and incident wavesCoefficient of transmission D – ratio of acoustic pressures of transmitted and incident waves

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Near field (Fresnel area) – this part of US beam is cylindrical – there are big pressure differences in beam axis

Far field (Fraunhofer area) – US beam is divergent – pressure distribution is more homogeneous

Increase of frequency of US or smaller probe diameter cause shortening of near field - divergence of far field increases

Acoustic parameters of medium: Near field and far field

• The adjacent points pressures effect each other. This effect is less in far field.

• Feynman derives the wave equation that describes the behaviour of sound in matter in one dimension (position x) as:

• Provided that the speed c is a constant, not dependent on frequency (the dispersionless case), then the most general solution is:

• where f and g are any two twice-differentiable functions. This may be pictured as the superposition of two waveforms of arbitrary profile, one (f) travelling up the x-axis and the other (g) down the x-axis at the speed c. The particular case of a sinusoidal wave travelling in one direction is obtained by choosing either f or g to be a sinusoid, and the other to be zero, giving:

• Where omega is the angular frequency of the wave and k is its wave number.

3D Wave Eq.

• Solution in cartesian coordinates: