bruno tte ultrasound
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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
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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
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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.
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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.
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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.
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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
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Wave direction
Longitudinal wave
Transversal wave
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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
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Sound speed in tissues
1480Water
330Air
4080Skull Bone
1600Muscle
1560Blood
1555Liver
1460Fat
600Lung
Speed (m/s)Tissue
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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)
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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
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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
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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
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Production of US
Piezoelectric effect
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Expansion
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-+
Contraction
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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
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Effect of cooling the unpolarizedcrystal in an electrical field
- + - +-+
- + - +
-+-+
- +-+
- +
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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
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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.
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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
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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
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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
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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
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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
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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
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Attenuation is exponential
Depth
SignalS= S0.e-kt
S/ S0=e-kt
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Attenuation expressed as dB/cm forthree tissues at various frequency
02468
1012
2 4 6 8 10
bloodlivermuscle
Frquence (MHz)
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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
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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
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How to measure distances using US
Measure the time transducer-interface-transducer
0 cm
6 cm
9 cm
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0 cm
6 cm
9 cm
t= 0 s
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0 cm
6 cm
9 cm
t = 20mm/1,540 mm.s-1
= 13 s
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0 cm
6 cm
9 cm
= 26 s
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0 cm
6 cm
9 cm
= 40 s
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0 cm
6 cm
9 cm
= 53 s
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0 cm
6 cm
9 cm
= 66 s
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0 cm
6 cm
9 cm
= 80 s
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0 cm
6 cm
9 cm
= 93 s
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0 cm
6 cm
9 cm
= 106 s
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0 cm
6 cm
9 cm
= 120 s
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A few consequencesfrom this very simple
experiment
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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
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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)
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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
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If q=90 Df=0
fr = f0
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If q=180 Df= - 2vf0/c
fr < f0
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Continuous wave doppler and pulseddoppler
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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
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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
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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)
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+1/2 PRF
-1/2 PRF
0
Laminar flow pattern
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+1/2 PRF
-1/2 PRF
0
Turbulent flow pattern
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+1/2 PRF
-1/2 PRF
0
+1 PRF
-1/2 PRF
0
Aliasing
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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
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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
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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)
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Aliasing in color!
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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
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Color Doppler
Power Doppler
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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.
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-70
-50
-30
-10
100 1 2 3 4 5 6 7 8 9 10
Frequency (MHz)
Power (dB)
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-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
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02468
1012
1 2 3 4 5 6 7 8 9 10Bub
bles
dia
met
er (
m)
Resonance frequency (MHz)
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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
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Physics of blood flow
(From Doppler measures tohaemodynamic parameters)
Different kinds of flow can be described: Laminar (a calm river) and Turbulent (a torrent)
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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
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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
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h1
v1
h2
v2
V
V
energy (2)=energy (1)
(rV)v12 + (rV)gh1 + P1.V=
(rV)v22 + (rV)gh2 + P2.V
P1P2
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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
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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)
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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
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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
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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.
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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 .
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