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10.0 The Physics of Ultrasound
Ultrasound is sound with frequencies higher than the highest
frequency that can be heard by human beings >20KHz).
Medical
ultrasound operates typically between 1 and 10MHz.
The
propogation characteristics are defined in the theory of acoustics and
medical ultrasound is principally concerned with compression waves
rather than shear waves.
•Basic acoustic physics, wave equation
•Plane, spherical wave solutions of the wave equation
•Wave propogation in media, energy, intensity, reflection, refraction
•Transmission, reflection coefficients, attenuation in media, scattering
•Doppler effect
•Beam formation and focusing
•Beam patterns, diffraction formulation
•Paraxial, Fresnel and Fraunhofer approximations
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View Full Document Important points from Ultrasound 1 Lecture
•Bulk compressibility,
•Ultrasound in tissue is principally a longitudinal (compressive) wave
•Wave equation in various geometries (plane wave, spherical wave)
•Speed of sound and density of various biological materials
•Acoustic Impedance
Z=ρc
•Acoustic Energy, Power Intensity.
•Transmission, Reflection for wave Amplitude and Intensity
•Quarter wave (λ/4) matching layer concept
dp
dV
V
1
1
c
Animation courtesy of Dr. Dan Russell, Kettering University
2
1
2
1
2
Z
Z
Z
Z
I
I
R
i
r
I
2
1
2
2
1
4
Z
Z
Z
Z
I
I
T
i
t
I
T
I
+ R
I
=1
(pressure is different!)
http://web.ics.purdue.edu/~braile/edumod/waves/WaveDemo.htm
L. Braile, Purdue University
)
2
cos(
0
ft
kx
u
u
)
2
cos(
0
0
0
ft
kx
cu
cu
p
)
2
sin(
2
2
0
ft
kx
f
u
f
iu
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View Full Document 0
2
p
c
2
2
2
2
1
t
p
c
p
u
dt
d
p
0
t
u
2
2
2
2
1
t
c
Summary
Wave Equations for
pressure or scalar
potential
velocity of sound, c
from
φ
we can calculate:
particle velocity
pressure
particle displacement
(by integration)
compression
2
0
)
(
c
p
s
for a particle velocity plane wave with
it is easy to show:
cu
p
0
)
2
(
0
ft
kx
i
e
k
i
c
u
s
/
f
iu
2
/
)
2
(
0
ft
kx
i
e
u
(so u
0
=φ
0
)
pure water has a very low attenuation loss compared to tissue
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1. Energy absorption (conversion to heat)
2. Scattering
3. Mode conversion (longitudinal to shear and back)
note that our modified plane wave no longer satisfies the wave equation
)
(
)
,
(
1
0
z
c
t
f
e
A
t
z
p
z
a
0
ln
1
A
A
z
z
a
The name given to the natural log of a ratio is Nepers.
Thus μ
a
is
in Np/cm (nepers/cm). If we use Np/cm for μ it is sensible to define
the attenuation coefficient that uses dB/cm with a different symbol,
α
a
a
e
686
.
8
)
(log
20
10
α is dependent on frequency, α=af
b
.
A safe assumption, medically,
being a linear dependence, ie, b=1.
where:
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This note was uploaded on 10/30/2010 for the course MP 230 taught by Professor Macfall during the Fall '10 term at Duke.
 Fall '10
 MacFall

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