Ultrasound Physics

VIBOT Edimburgh, Le Creusot, Girone

F. Brunotte, professeur, Biophysics, Nuclear medicine. Le2i Laboratory, Nuclear medicine division Centre G-F Leclerc,

Magnetic resonance imaging, Academic Hospital Dijon

Francois.Brunotte@u-bourgogne.fr

Content

Introduction Sounds Production of Ultrasounds Attenuation of US in the tissues How to measure distances in the tissues using US Modes A, B ( 2D and TM) Doppler Fluids physics Bioeffects and safety considerations

Definition of sound

Nearly all of us have an idea of what soundis because of our ability to hear.

Familiar description such as sound is thesensation perceived by the sense ofhearing is limited

At a fundamental level: sound ismechanical energy transmitted by pressurewaves in a material medium.

Ultrasound- definitions Sound is a form of energy which is said to be mechanical,

meaning it exists in the form of physical movement of themolecules and particles in the medium.

Sound energy differs from electromagnetic energy (light,X-Rays) which can travel through a vaccuum

As a consequence, definition of sound includes the factthat they propagates through a material medium Sound waves only exist in media containing molecules (or

particles ) such as air, water and various tissues in the body.

Sound production

The source of sound is a vibrating object.One example is a tuning fork which vibrateswhen you strike it. It pushes and pulls against adjecnet molecules

from the air causing them to vibrate . Thesevibrating molecules then causes furhteradjacent molecules to vibrate and so forth.

Sound propagation includes The back and forth displacement of the molecules (or

particles) squeezes and pulls on the further particles of themedium. Places where the molecules are pushed together are called regions

of compression. The medium density is slightly greater than in themedium if the wave were absent

Places where the molecules are drawn apart are called regions ofrarefaction with a lighly lower medium density

Waves can be Longitudinal, i.e. more or less parallel to the direction the sound is

propagated Transversal, i.e perpendicular to the direction of the sound

Wave direction

Longitudinal wave

Transversal wave

Sound speed The speed of sound is determined primarily by

the charactersitics of the medium (other factorssuch as frequency are so small that they can beneglected) K=Bulk modulus which reflect the stiffness of the

material, that is the resistance of the material to becompressed (N/m2) and r= medium density (kg/m3)

122

3

22

3

2

../

/..// --- ===== smsm

mkgmsmkg

mkgmNKc

r

Sound speed in tissues

1480Water

330Air

4080Skull Bone

1600Muscle

1560Blood

1555Liver

1460Fat

600Lung

Speed (m/s)Tissue

Waves: frequency, speed andwavelength

Given c , the speed of the ultrasound, and fits frequency its frequency, the wavelengthl isl=c/f

The average speed of sound in soft tissue(exept the lung)1540 m/s

The wavelength at 3 MHz is 1540/3 106(0,5 mm)

Content

Introduction Sounds Production of Ultrasounds Attnuation of US in the tissues How to measure distances in the tissues using US Modes A, B ( 2D and) TM Doppler Fluids physics Bioeffects and safety considerations

Ultrasound transducer

The term transducer refer to any devicethat is used to convert signals or energyfrom on form to another.

Most of transducers respond to theparameter of interest by converting detectedvalues into electrical signal.

An ultrasonic tranducer converts acousticenergy into electrical signal and vice versa

The piezoelectric effect

The piezoelectric effect was discovered by twobrothers Pierre and Jacques Curie. They found thata force applied to a quartz results in an electricalsignal

Pierre Curie was awarded the Nobel prize but notfor this research in the field of ultrasound. Despite the medical value of ultrasound imaging , no

Nobel prize has distinguished this field of physics

Production of US

Piezoelectric effect

+-

Expansion

-+

Contraction

Different crystals for ultrasoundproduction

Quartz and tourmaline are piezoelectric crystals In diagnostic ultrasound these crystals have been

widely replaced by Piezoelectric ceramic transducer elements

Lead zirconate titanum: It is a mixture of crystals randomly oriented Relatively easy to shape the crystal into various forms such as

planar or concave disks The crystal is heated above the Curie temperature and te a high

voltage is applied before and during cooling the crystal Then the crystal remains polarized and exhibit piezoelectric

properties

Effect of cooling the unpolarizedcrystal in an electrical field

- + - +-+

- + - +

-+-+

- +-+

- +

Frequency properties of thetransducer

1) The resonance frequency is determinedby the frequency of the electrical pulseapplied to the crystal.

2) The phenomnenon is reverted when thetransducer is used as a receiver

A single resonance frequency orseveral?

A piezoelectric crystal has a resonance frequencyat which it is more efficient in convertingelectrical energy into mechanical energy

Some broadbandwidth transducers are designed tobe operated at several different frequency. Thechoosen frequency is selected by shapingtheelectrical pulse applied to the transducer.

Transducer arrays Nowadays, these transducers are used rather than

single-element transducer. These transducers are made by grouping closely

piezoelectric elements which have their ownelectrical connection. This makes possible toexcite these small elements individually or bygroup or following a given sequence.

Beam focusing Beam steering

Attenuation of ultrasounds inbiological media

As a sound beam goes through tissue, itsintensity decreases as a function of distance.

Sources of attenuation Reflection Refraction Absorption

US intensity reflection coefficient when theincidence is perpendicular to the interface

Tissue 1

Tissue 2

Incident beam

Transmitted beam

Reflected beam

Ir/Ii=(Z1-Z2)2/(Z1+Z2)2

Interfaces inducing a high reflectioncoefficient

Two cases have to be emphasized: Interface in which one medium is air

Air between the transducer and the patient skinshould be avoided, since almost 100% of theincident energy would be reflected

This explains the need for a coupling gel between theultrasound transducer and the patient during ultrasoundexamination

Ultrasound imaging through the lung s almost impossible

Interface in which one medium is bone Soft tissue-to-bone is a strong reflector

Whenever possible, transmission through bone is avoidedin diagnostic ultrasound

Impedance of different tissues

7,8Bone

1,71Muscle

1,65Blood

1,34Fat0,18Lung

0,0004Air

Impedance (106 kg.m-2.s-1)Tissue

Multiplying density time speed: Z=r.c

Tissue 1

Tissue 2

Incident beam

Transmitted beam

Reflected beamqi qr

qt

qr=qiqt varies according to the kind of interface

and especially the difference of speed ofsound on the two sides of the interface

Attenuation is exponential

Depth

SignalS= S0.e-kt

S/ S0=e-kt

Attenuation expressed as dB/cm forthree tissues at various frequency

02468

1012

2 4 6 8 10

bloodlivermuscle

Frquence (MHz)

Content

Introduction Sounds Production of Ultrasounds Attnuation of US in the tissues How to measure distances in the tissues using US Modes A, B (2D and TM) Doppler Fluids physics Bioeffects and safety considerations

Mode A

(amplitude)

Mode B

(brillance=

brigthness)

Echo display modes

A trace that show the echo signalamplitude versus time (depth)

Display intensity modulated dotson the screen

How to measure distances using US

Measure the time transducer-interface-transducer

0 cm

6 cm

9 cm

0 cm

6 cm

9 cm

t= 0 s

0 cm

6 cm

9 cm

t = 20mm/1,540 mm.s-1

= 13 s

0 cm

6 cm

9 cm

= 26 s

0 cm

6 cm

9 cm

= 40 s

0 cm

6 cm

9 cm

= 53 s

0 cm

6 cm

9 cm

= 66 s

0 cm

6 cm

9 cm

= 80 s

0 cm

6 cm

9 cm

= 93 s

0 cm

6 cm

9 cm

= 106 s

0 cm

6 cm

9 cm

= 120 s

A few consequencesfrom this very simple

experiment

The attenuation of ultrasounds in depth is important andmakes echoes returning from structures at large distancesfrom the transducer weaker than echoes from nearbystructures.

Sound beam attenuation is compensated by using TGC(Time Gain Compensation) and DGC (Distance GainCompensation)

A given crystal cannot works simultaneously as anemitter and a receiver Ultrasounds are usually emitted in a pulsed manner (referred as

pulse-echo mode).

Duty factor is the fraction of time thetransducer actively transmits sound

P.R.F. is Pulse repetition frequency

0 cm

6 cm

9 cm

Travel time (and return) to 9cm depth# 120 s

PRF= 1/120 10-6 s

= 8333 s-1 (Hz)

Axial resolution is depending onthe echoes train length

Pulse duration (PD) = Nc x T

En s = Nc / f(MHz) at 3 MHz

PD= 1s

Resolutionf0

If q=90 Df=0

fr = f0

If q=180 Df= - 2vf0/c

fr < f0

Continuous wave doppler and pulseddoppler

What are the differences betweencontinuous wave and pulsed

doppler? Continuous:

Large range of measurable bloodflow speed,

Unknown depth Pulsed

Limited measurable speed,Depth is known precisely

Sampling theory tells us that thehighest doppler frequency shift shouldbe less than half of PRF

PRF= c/2D et 1/2 PRF = c/4DDf=2vf0cosq/c

v

Spectral analysis

The reflected signal comprised manyfrequencies varying according the angle, thevelocity of the blood and the size of thedoppler sample volume if pulsed doppler isemployed

A quantitative analysis showing thedistribution of frequencies is done byspectral analysis (Fast Fourier Transform)

+1/2 PRF

-1/2 PRF

0

Laminar flow pattern

+1/2 PRF

-1/2 PRF

0

Turbulent flow pattern

+1/2 PRF

-1/2 PRF

0

+1 PRF

-1/2 PRF

0

Aliasing

If moving the baseline to -1/2PRF, TheFourier transformation allows tomultiply by a factor 2 the maximumfrequency which can be recorded.

In the previous example (fo=3MHZ,depth=8cm and doppler angle=0), themaximum velocity which can berecorded moves from 1.2 m/s to 2.4m/s

How to improve the contrastbetween flowing blood and

stationary tissues? The main concept is to take advantage of

the doppler shift from US reflected by theflowing blood.

The small frequency shift is color-coded

Color Doppler Doppler scanning of the frame

A color image is superimposed on a B_Modeimage in gray levels. The color reflects the flowdirection and the calculated speed ( dependingon the doppler angle)

Aliasing in color!

Doppler power mode ignores the reflector velocityinformation but estimates the total strength of theDoppler signal.

Any Doppler shifted signal , regardless of thefrequency of the shift contributes to the pixel data.

The net signal is related to the number of red bloodcells moving regardless of their velocity.

In power mode, the image does not varysignificantly with the direction of the flow withrespect to the ultrasound beam.

Doppler power or energy

Color Doppler

Power Doppler

How a large frequency differencecan be obtained between stationary

tissues and flowing blood?

Imaging the tissue at harmonic of thefrequency used for the incidentultrasound beam.

-70

-50

-30

-10

100 1 2 3 4 5 6 7 8 9 10

Frequency (MHz)

Power (dB)

-70

-50

-30

-10

100 1 2 3 4 5 6 7 8 9 10

Frequency at receiver (MHz)

Power (dB)

Ultrasound beam at 3,2 MHz

02468

1012

1 2 3 4 5 6 7 8 9 10Bub

bles

dia

met

er (

m)

Resonance frequency (MHz)

Content

Introduction Sounds Production of Ultrasounds Attenuation of US in the tissues How to measure distances in the tissues using US Modes 2D et TM Doppler Fluids physics Bioeffects and safety considerations

Physics of blood flow

(From Doppler measures tohaemodynamic parameters)

Different kinds of flow can be described: Laminar (a calm river) and Turbulent (a torrent)

Continuity equation (flow conservation)

Compute A1 in the case V1, A2 and V2 can bemeasured

A1V1 A2

V2Flow = A1.V1=A2.V2A1=A2.V2/ V1

Bernoullistheorem

The Bernoulli effect is simply a resultof the conservation of energy.

In a flowing fluid,in the absence ofloss of energy through friction, the sum

of kinetic energy+gravific energy+work of pressure remains constant

h1

v1

h2

v2

V

V

energy (2)=energy (1)

(rV)v12 + (rV)gh1 + P1.V=

(rV)v22 + (rV)gh2 + P2.V

P1P2

h1

v1

h2

v2

V

V

Assuming that both points are at the sameheight and by dividing both members by V

rv12 + P1= rv22+ P2The sum of static pressure

and dynamic pressure is constant

P1P2

DP= r.(v22 - v12)

r= 1000 kg/m3

1 mm Hg= 133 Pa

DP=4.v22

mm Hgm/s

When the staticpressure of theblood drops, forexample at thelevel of a stenosis,the static pressureis converted intodynamic pressure.

(By neglecting V1 in front of V2)

Content

Introduction Sounds Production of Ultrasounds Attenuation of US in the tissues How to measure distances in the tissues using US Modes 2D et TM Doppler Fluids physics Bioeffects and safety considerations

Bioeffects and safety considerations

It is known that Ultrasound beams candamage tissues.

Contrasting with that, the use of diagnosticultrasound equipment has never beenreported to have injured any patient.

The effects of low-level ultrasound onbiological tissue remain to be investigated

Mechanisms involved in inducingbioeffects of ultrasounds

Heating A sound beam which is propagated through a tissue is attenuated.

A large part of attenuation is due to absorption i.e. conversion ofthe ultrasonic energy into heat.

Cavitation Intense ultrasound beams in a fluid can generate tiny bubbles from

dissolved gases in the fluid Pulmonary haemorrhages observed in the rat and in the monkey

with pulse acoustic beams are usually explained as an effect ofcavitation in alveolar gas

Non cavitation mechanical effects Biological effects have been produced in experimental models of

plants and cells in condition where no rise of temperature occurredas well as no cavitation effect.

It is thought that these effects are associated with mechanicaldisplacements, acceleration and stresses on particles in themedium.

Field of interest for further reading

3D Ultrasound imaging Artifacts and the way to eliminate them Contrast agents for eultrasound imaging Image processing Ultrasound equipment quality insurance Wall motion analysis using ultrasound .