Transcript ultrazvuk - University of Zagreb Medical Studies in English
October, 2008 J.Brnjas-Kraljević
Sound waves
sound wave
oscillation – transport of mechanical energy of particles of elastic medium through space - by
audiable
sound -
infrasound
frequency range 20 Hz to 20 kHz frequency range 20 Hz resonance of inner organs
ultrasound
frequency range > 20 kHz - resonance of molecules
Nature of the sound wave
transport of the source
–
mechanical energy of oscillation
body oscillating in the elastic medium energy of oscillation is transferred through space with
speed
wavelength
v
T
f
frequency elastic medium is requisite for the existence of sound-mechanical wave
elongation time molecule
2D presentation of the wave
wave length particle is oscillating in the direction of wave propagation in the medium appear the regions of compression and rarefaction, i.e. with higher and lower pressure direction of motion
Equation for harmonic wave
the change of elongation in space and time at point M the oscillation is late by t’ with source oscillation
x
x
A sinω
t t'
what is the angle value for this time interval
A sin
t '
ω
r v
r t v
t '
A sin
2
π
phase shift
t T r λ
x
A sin(
t
kr ) k
2
- wave number
Acoustic pressure
the change of acoustic pressure:
p a
p a 0
10
5
Pa
sin(
t p a
kr
10
Pa
intensity of harmonic wave :
) I
E St E
1 2 m
2 A 2
in diagnostics I = 10 – 100 mW/cm
2
Intensity of sound wave
I
1
2 2 A 2
v
acoustic impedance of medium properties of source
I
p 2 a 0 2 Z
intensity of spherical wave decreases with r 2 plane waves are better for diagnostics
I 2 I 1
I 1 r 1 r 2 I 2
r 1 2 r 2 2
Ultrasonic wave
frequency > 20 kHz, in medicine 1-20 MHz source: piezoelectric crystal crystal in electric field oscillates with frequency of alternating field E = E 0 sin t d = d 0 sin t source if stimulated to oscillation by mechanical force - the alternative voltage can be measured at the crystal opposite surfaces F = F 0 sin t U = U 0 sin t detector thickness is determined by wave frequency – resonance
Piezoelectric effects
piezoelectric effect – induction of electric charges on the surface of the crystal, which is elastically deformed by external force change of deformation direction changes the direction of piezoelectric materials are: quarc (SiO 2 ), tourmaline, different ceramics and some polymers polarization
Piezocrystal is source and detector
isolator piezo-crystal adjustment layer thickness of crystal is /2 under resonance condition – the intensity of sound wave is the highest the adjustment layer – thickness is /4 – maximal energy transfer into the tissue impedance adjustment Z 2 layer = Z c xZ b additional layer of gel removes air bubbles pulse methods – wave energy is transferred in pulses Pulse – defined amount of energy sound isolator – blocks the sound propagation in other directions directed plane wave
Ultrasound probe
in diagnostic praxis the frequency is between 2 and 20 MHz.
attenuation and absorption increases with frequency of sound the choice of best frequency - compromise between better resolution and smaller absorption resolution increases with increase of frequency absorption increases with increase of frequency higher frequencies for surface organs lower frequencies for deeper structures
SPL – space length of pulse –n
PD - time interval – n/
n
PRF – frequency of repetition
time
frequency/MHz SPL /mm PD /
m
s
2,5 5,0 7,5 10,0 1,8 0,9 0,6 0,45 1,2 0,6 0,4 0,3 highest I = 1 W/cm 2 average (SA) =0,3 W/cm 2 transductor width pulse length is 2 to 3 sonic beam is not homogeneous in space – there is a distribution of energy SPL is changed in tissue – stronger absorption of higher frequencies – the resolution is worse at the spot deeper in the body PRF - 2-3 kHz – it must be enough time to detect all reflected waves – v/2D D - depth of imaging determines the resolution
Axial and lateral resolution
resolution is determined by configuration of sound field, it is changed with depth in tissue resolution is limited with – for 3,5 axial resolution – distance between beam – about 2 lateral resolution – distance between two parallel planes – depends on the width of beam - about 10 resolution is better for the structures closer to the source distance from the surface higher frequency – longer Fresnel's zone – better resolution – stronger absorption!
Z f =a 2 /
Transmission depends on ratio of acoustic impedances
R A
0 1
,
48 1
,
48
x
10 6
x
10 6 430 430 0
,
9994 air water a u a r a
t
Z 1 1 Z 2 2
I r I
0 1
,
48
x
10 1
,
48
x
10 6 6 430 430 2 0
,
9988
T A
0 2
x
1
,
48
x
10 6
x
430 1
,
48
x
10 6 430 0
,
0046
I t I
0
(
4
x
1
,
48
x
10 6 1
,
48
x
10 6
x
430 430
)
2 0
,
0012
Reflection and transmission
law of reflection:
angle of reflection = angle
sin
a 1
sin
a 2 law of refraction: coefficients of reflection and transmission: r + t =1
v
1
v
2
r
I I r
0
Z
1
Z
1
Z Z
2 2 2 2
t
I I t
0
Z
4 1
Z
1
Z
2
Z
2 2 for Z 1 for Z 1 Z 2 Z 2 maximum transmission ili Z 1 Z 2 maximum reflection
Speed and acoustic impedance
speed/ms -1 impedance/kgm -2 s water air 1484 343 blood 1550 myocardium 1550 fat liver kidney bone 1450 1570 1560 3360 1,48 x 10 -6 0,0004 1,61 x 10 -6 1,62 x 10 -6 1,38 x 10 -6 1,65 x 10 -6 1,62 x 10 -6 6,0 x 10 -6 absorption at 1 MHz /dBcm -1 0,000029 0,159 0,0023 0,040 0,0069 0,0126 0,0104 0,1496
Intensity level
we do not need absolute value of intensity but its ratio over referent intensity
10
log
I I
0
unit is decibel (dB) I 0 = 10 -12 Wm -2 20 dB is decrease in intensity 100 times
I 0
Attenuation of sound wave in matter
I 1 I 2 I=I 2 -I 1 =k I 1 x -dI=k I dx I x
dI
k dx I I
0
I
I dI I I
0
e
kx
k
0
x dx
Absorption of sound wave
I
A
A 2 which means: half value layer x 1/2 I(x 1/2 ) = I 0 /2
A
0
e
a
x I
I
0
e
2
a
x
is determined with
x
1
/
shorter half value layer means better absorber
2
ln
2 2
a
Basics of ultrasound diagnostics
wave energy in tissue is partially lost due to absorption and scattering part of energy is lost due to reflection at the boundary of two tissues the images are formed from the beams reflected of plane surfaces additional information could be obtained from scattered waves caused by tissue inhomogeneity it is possible to detect the changes in elastic properties of tissues (consequence of sickness) elasticity of tissue – connective tissue – high acoustic impedance– blood cells have high impedance – observable in the image tissue of low transparency - tumors in solid tissue – acoustic shadow - simple diagnosis
Doppler's effect
the consequence of source or detector motion is apparent change in detected frequency frequency shift can be observed if the speed of moving object is lower than the speed of sound wave approach to the source higher frequency
v
v f
f z p p i v
departure from the source lower frequency
z v z
p f
f
simultaneous approach
p i v z
f
f
0
v p v
v i z
Ultrasound diagnostics
reflection of wave at the boundary of two different media the intensities of reflected waves are recorded as a function of time the image is the distribution of boundaries that are perpendicular to the incident wave by moving the probe we can record more parallel cross sections - by simultaneous use of more probes we can record the whole body
A, B and M mode
( the way of presentation)
A mode
intensity of reflected wave is presented with amplitude
B mode -
intensity of reflected wave is presented with the brightness of the point; wave of higher intensity – more shining spot on the screen
M mode
used for visualization of moving boundaries, specially heart; it is combination spatial image of echo waves and temporal graphical display
Image generation
A mode B mode t
t
intensity of reflected wave depends on impendency difference higher intensity means larger difference temporal interval of incoming signals is proportional to the distance of reflecting surfaces in B-mode – higher intensity, due to bright points, but lower resolution grey scale – bimodal display each pixel is characterized by number, higher number means stronger reflection pixel depth has influence on image contrast
2D images
cross sections which are recorded are the planes perpendicular on the beam we use the B-mode display: grey scale depends on echo intensity – the boundaries of different tissues are white B-mode, the depth depends on probe parameters the number of lines in the image is equal to the number of units in the probe image is reconstituted – frame of speed if it is high – we get the image in "real time"
probe pulse mode mode
“
Real time”
simultaneous recording with more independent beams, each has a width 1-4 , dependence on frequency wave front – in Fresnel zone has the size of probe cross section the length of lines determines the depth of the image linear transducer- parallel lines of recording, large aperture, it is not for the heart; sequential starting aperture – the size of transducer or the number of synchronized elements phase beam - one sector of space is recorded, line density is decreasing with distance– complicated display, but with smaller window– frequencies 2-10 MHz image depth is primary determined by attenuation
of pulse Amplifier probe Amplifier Signal processor
Measurement of flow
echo
the motion is heard as sound signal Pulse Doppler – pulse source determines the depth of reflection frequency analysis is limited on temporal interval “gating”
by prof.A.Kurjak