AIA-DAGA 2013 Merano
Experimental apparatus for the measurement of the ultrasound attenuation
coefficient
Chiara Musacchio, Rugiada Cuccaro, P. Alberto Giuliano Albo, Simona Lago, Adriano Troia
Istituto Nazionale di Ricerca Metrologica, 10135 Torino, Italy, Email: [email protected]
with n that varies between 1 and 2.
Introduction
Materials and Methods
Measurements of acoustic properties of materials at
ultrasonic frequencies is of great interest for many fields,
ranging from medical applications to building acoustic.
The experimental apparatus
In the present work, measurements are carried out in a water
tank with the following dimensions: 12 cm of width, 12 cm
of height and 50 cm of length.
At INRiM’s Thermophysical Laboratory, an experimental
apparatus for the measurement of the ultrasonic attenuation
coefficient is currently being implemented. Used
measurement method consists of the amplitude comparison
of an ultrasonic tone burst signal, got through a reference
material, with that one propagated into the sample under test.
Frequency analysis of the received signals is carried out in
order to compare the amplitudes at specific frequencies.
Different transducers are used to cover the frequency range
of interest.
The entire apparatus (shown in Figure 1), including tank,
transducers and sample, is thermally insulated from the
environment by means of a case of 4 cm thick walls of
polyurethane foam.
Temperature inside the liquid bath is measured with a
platinum resistance thermometer, whose 4-wire resistance is
read by a Kheitley 2000 multimeter.
In this work, a description of the apparatus and
measurements, carried out on gels mimicking biological
tissues in the frequency range between 1 and 10 MHz, are
presented.
Ultrasonic attenuation coefficient
Sound waves are subjected to energy loss during their
propagation in a medium. This attenuation is essentially
caused by absorption and scattering phenomena. Assuming
I0 the initial mean temporal intensity, the value I(x) at a
distance x along the acoustic path can be expressed as
[W·cm-²]
𝐼𝐼(𝑥𝑥) = 𝐼𝐼0 𝑒𝑒 −2𝛼𝛼𝛼𝛼
(1)
where α is the attenuation coefficient of the intensity. The
value of α is commonly expressed in decibel and,
considering the quadratic proportionality between intensity
and pressure p, it can be expressed as:
[dB·cm-1]
1
𝐼𝐼(𝑥𝑥) 1
𝑝𝑝(𝑥𝑥)
α= 10∙Log
= 20∙Log
𝑥𝑥
𝐼𝐼0
𝑥𝑥
𝑝𝑝0
Figure 1: Diagram of the experimental apparatus.
(2)
The acoustic field produced by ultrasound plane circular
transducer can be divided into two regions, called near-field
(Fresnel diffraction zone), where the intensity of the acoustic
field has a complex structure, and far-field (Fraunhofer
diffraction zone), in which the acoustic field becomes
simpler and the axial intensity proceeds to decrease
approximately as the inverse square of distance [3].
The value of the attenuation depends on the kind of the
medium and the sound wave frequency. For example,
attenuation in liquidsis mainly driven by viscous and
relaxing phenomena and it can be expressed as:
𝛼𝛼 = 𝛼𝛼0 𝑓𝑓 2
[dB·cm-1]
-1
(3)
Accounting for these considerations, the measurement
system has been designed so that signals propagate beyond
the near-field limit.
-2
where α0 is expressed in dB·cm ·MHz [1].
Biological media are characterized by frequency dependence
of the attenuation with much more complex expression.
Results of Bamber (1998) [2] show that, for a large part of
soft tissue, the expression of attenuation as a function of
frequency is given by:
𝛼𝛼 = 𝛼𝛼0 𝑓𝑓 𝑛𝑛
[dB·cm-1]
Measurement procedure
A tone-burst signal is generated and sent to the transmitter
transducer and it is received at the opposite side of a tank by
the second transducer. Pairs of Olympus Panametrics
hydrophones have been used as source and receiver
transducers as shown in Table 1.
(4)
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Model
V312
A302S
A304S
Diameter
0,25 in
1 in
1 in
Frequency
10 MHz
1 MHz
2,25 MHz
So far, the decrease of the signal amplitude is supposed
caused by sample attenuation processes. However, the
effects of mismatching at different materials interfaces have
to be considered.
The loss of signal at the interface between water-sample and
between sample-water has been calculated considering the
different values of impedance of the media and calculating
transmission coefficients at the interfaces.
Impedance of water, Zw, is obtained using the water density
at ambient temperature (measured during the acquisition)
and pressure, and calculating the speed of sound from
Marczak's equation [5]. Sample impedance, Zs, is calculated
from the density measurements performed at INRiM
Mechanics Division and using the direct speed of sound
measurements.
In the first part of the measurement procedure, the burst
signal goes through a water path and is received by the
second transducer. After that, the sample is inserted in the
sound path and the burst reaches the receiver crossing water
firstly, the sample and then water again. The received signals
voltage are acquired respectively when the tank is filled with
water only Vw(t), and when the sample is inserted in the tank
Vs(t).
Transmission coefficient between water and sample and
between sample and water are obtained respectively using
the following equations:
Data Analysis
Attenuation coefficient, as function of the frequency, is
calculated using equation (1).
𝑇𝑇𝑤𝑤 −𝑠𝑠 =
The received signals are processed in the way described
below for determining amplitudes As and Aw. Considering
the received signals V(t), its Fourier transform C(f) is
calculated at a specific frequency fi as:
2𝑍𝑍𝑠𝑠
𝑍𝑍𝑠𝑠 + 𝑍𝑍𝑤𝑤
𝑇𝑇𝑠𝑠−𝑤𝑤 =
(8)
2𝑍𝑍𝑤𝑤
𝑍𝑍𝑠𝑠 + 𝑍𝑍𝑤𝑤
(9)
The received signal is corrected in order to delete the effect
of the amplitude decrease due to the interfaces and the
amplitude A* is calculated as:
(5)
− 𝑖𝑖 � 𝑉𝑉(𝑡𝑡) ∙ sin(2𝜋𝜋𝑓𝑓𝑖𝑖 𝑡𝑡) 𝑑𝑑𝑑𝑑
𝐴𝐴∗s (𝑓𝑓𝑖𝑖 ) =
In-phase and in-quadrature components of the signal at a
specific frequency are respectively the real and imaginary
part of C(fi). The square root of in-phase and in-quadrature
quadratic components is proportional to the amplitude of a
specific frequency component of the signal.
[V]
(7)
Corrections
Whereas the transducer with 10 MHz centre frequency is
broad band and it is used to generate burst at 10, 8, 6, 5, 4
and 2 MHz, the other two pairs of transducers are used at
their resonance frequency of 1 and 2,25 MHz. Voltage signal
is generated by a function generator and the receiver
transducer is connected to a digital oscilloscope LeCroy
Wave Runner 62Xi for processing and signal acquisition.
Tone bursts are 10 cycle long and 10 V (peak to peak
voltage) of amplitude.
A( f i ) ∝ C ( f i )
[dB·cm-1]
where Ls is the thickness of the sample.
Table 1: Model, diameter and resonance frequency of the
used transducers.
𝐶𝐶(𝑓𝑓𝑖𝑖 ) = � 𝑉𝑉(𝑡𝑡) ∙ cos(2𝜋𝜋𝑓𝑓𝑖𝑖 𝑡𝑡) 𝑑𝑑𝑑𝑑
𝐴𝐴s (𝑓𝑓𝑖𝑖 )
1
20 ∙ Log
𝐴𝐴w (𝑓𝑓𝑖𝑖 )
𝐿𝐿s
𝛼𝛼(𝑓𝑓𝑖𝑖 ) =
𝐴𝐴s (𝑓𝑓𝑖𝑖 )
𝑇𝑇s−w ∙ 𝑇𝑇w−s
[V]
(10)
The quantity As* is the amplitude used in the calculation of
α(fi ) in formula (7).
Preparation of tissue mimicking
materials (TMMs)
Formulations for TMMs preparation have been chosen
among different recipes reported in last years in this field
[6,7]. In particularly, a Phytagel TMM and two Agar based
TMMs have been prepared.
(6)
Acquired signal is sampled and consists in a vector V(ti ),
where the index i represents the number of samples for each
acquired signal. The used sampling rate of the oscilloscope
is 5 GSample/s. Integrals in Eq. 5 are calculated via Bode
integration method.
Tissue mimicking materials have been prepared considering
that the total attenuation could be given by the presence of
absorbent - like long chain polysaccharides (chitosan) - or
scattering agents (in this case silicon carbide). In order to
investigate the absorption due to chemical relaxation
processes or from the presence of solid particles, these two
case have been explored using Agar and phytagel as polymer
matrix. First TMM was prepared by mixing a 2% in weight
aqueous solution of Phytagel with Ca2SO4 (0,5% in weight).
The solution was heated at 90 °C, then, while the solution
was left to cool, a specific amount of SiC (1% in weight)
Appling this calculation to Vw(t) and Vs(t) signals, the
respective amplitude Aw(fi) and As(fi ) are obtained and used
as measurement of the frequency component amplitude of
the received signal.
The attenuation is then calculated as:
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was added to increase attenuation. Before the polymerisation
reaction is completed, the sample was cast into a cylindrical
mould used for acoustic characterization. The second TMM
was based on Agarose polymer, an aqueous solution of Agar
(3% in weight) heated at 90 °C and then cast into a
cylindrical mould. In this case, benzalkonium chloride has
been added (0,9% in weight) as an antibacterial and
antifungal agent. The third TMM was based on Agarose
polymer (3% in weight) to which Chitosan (2% in weight)
has been added in order to explore the adsorption given by
other long chain polysaccharide. Since the chitosan is
insoluble at pH > 6,0, an acid buffer of sodium acetate has
been used as host solution. From this point, these TMM will
be called respectively Gel 1, Gel 2 and Gel 3.
Figure 3: Attenuation coefficient values as a function of
frequency. Interpolating curve parameters (equation (4)):
Gel 1 (α0 = 0,23 dB·cm-1·MHz-1,2; n = 1,2);
Gel 2 (α0 = 0,04 dB·cm-1·MHz-1,5; n = 1,5);
Gel 3 (α0 = 0,03 dB·cm-1·MHz-1,5; n = 1,5).
A prospective apparatus for attenuation
measurement in solids
Figure 2: Gel samples. From left to right: Gel 2, Gel 1,
Gel 3 are shown.
Preliminary study has been conducted on a different
apparatus for attenuation measurement.
Measurements Results
An ultrasonic transducer has been coupled by a BK7 optical
glass buffer rod to the sample under test. The buffer rod
length the avoids near-field condition measurements.
The measurement results of attenuation coefficient for the
investigated gels are reported Figure 3. Fitting curve to
interpolate the results with the power law expected in
equation (4) are also evidenced. The obtained values
evidence that addiction of scattering agent, as silicon
carbide, gives a significant contribution to attenuation while,
in the present recipe, the presence of long chain
polysaccharide does not improve the attenuation coefficient
of the gel.
Source Transducer
Received echoes
V1(t) V2(t)
Uncertainty budget
Results uncertainties can be obtained combining
contributions of main sources listed in Table 2. As it can be
observed, almost all the budget contribution is due to the
thickness measurement. It depends on the difficulty to
measure the dimensions of soft-solid materials and on the
gel surface irregular shape.
Quantity
air
Figure 4: Measurement apparatus and diagram of the
acoustic signal path.
The signals used for calculating attenuation are the two
echoes coming from the interface between glass and sample
and the surface of the sample exposed to air. Attenuation of
the first echo, V1(t), is only due to acoustic path in optical
glass, while the second echo, V2(t), is attenuated by both the
acoustic path in optical glass and in the sample. So, the
different amplitude of the two signal can be ascribed to
sample properties.
Relative uncertainty
Thickness, L
Density
1,43%
0,10%
Speed of sound
V(t) measurement
1,45%
0,98%
Overall uncertainty
2,8%
Table 2: Contributions to the uncertainty budget.
The signal amplitude A related to the acquired signal V(t) is
evaluated as described in “Data Analysis”.
As done before, corrections for different impedances effects
have to be taken into account. Reflection at the interface
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buffer rod-sample affects the amplitude A1 of the first signal.
To remove this effect, the amplitude A1 is replaced with A1*:
𝐴𝐴∗1 =
𝐴𝐴1
𝑅𝑅BR-s
[V]
(11)
[V]
(12)
[dB·cm-1]
(13)
uncertainty budget, with the determination of the uncertainty
associated to the calculation method and improvement of the
thickness measurements, is in course of definition.
Buffer-rod system is promising for measurements in solid
materials and will be improved with the assessment of
calculation and corrections related to divergence of the field
in the sample.
where RBR-s is the reflection coefficient.
The second signal A2 is corrected by:
𝐴𝐴∗2 =
𝑇𝑇𝐵𝐵𝐵𝐵 −𝑠𝑠
𝐴𝐴2
∙ 𝑅𝑅s-air ∙ 𝑇𝑇𝑠𝑠−𝐵𝐵𝐵𝐵
Acknowledgments
The research leading to these results is conducted in the
frame of the EMRP JRP HLT03. The EMRP is jointly
funded by the EMRP participating countries within
EURAMET and the European Union.
The attenuation is calculated as:
𝛼𝛼(𝑓𝑓𝑖𝑖 ) =
1
𝐴𝐴∗2 (𝑓𝑓𝑖𝑖 )
20 ∙ Log ∗
𝐿𝐿s
𝐴𝐴1 (𝑓𝑓𝑖𝑖 )
References
[1] Pinkerton, J.M.M.: The absorption of ultrasonic waves in
liquids and its relation to molecular constitution.
Proc. Phys. Soc. B62 (1949), 129-41
Preliminary results in Plexiglas
Preliminary measurements have been made in Plexiglas
sample in a frequency range between 2 and 5 MHz. The
obtained results are shown in Figure 5.
[2] Bamber, J.C.: Ultrasonic properties of tissues in Duck,
F.A., Baker, A.C., Starritt, H.C., ”Ultrasound in medicine“
IOP, London (1998), 57-88
[3] Hill, C.R., Bamber, J.C., ter Haar, G.R.: Physical
principles of medical ultrasonics, John Wiley & Sons, Ltd.
(2004)
[4] Humpfrey, V.F., Duck, F.A.: (1998). Ultrasonic fields:
structure and prediction, in Duck, F.A., Baker, A.C., Starritt,
H.C., ”Ultrasound in medicine“ IOP, London (1998), 3-22
[5] Marczak, W.: Water as a standard in the measurements
of speed of sound in liquids.
J. Acoust. Soc. Am. 102 (5) (1997), 2776-2779
[6] Ramnarine, K.V., Anderson, T., Hoskins P.R.:
Construction and geometric stability of physiological flow
rate wall-less stenosis phantoms.
Ultrasound Med. Biol. 27 (2001), 245–250
Figure 5: Attenuation coefficient values measured in
Plexiglas at 2, 3, 4, 5 MHz.
[7] King, R.L., Liu, Y., Maruvada, S., Herman, B.A., Wear,
K.A., Harris, G.R.: Development and characterization of a
tissue-mimicking material for high-intensity focused
ultrasound.
IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 58 (7)
(2011), 1397-405
As suggested in [8], a linear dependence with the frequency
f, a fitting line has been calculated as:
α = a + α0f
[V]
(14)
[8] Zhao, B., Basir, O.A., Mittal, G.S.: Estimation of
ultrasound attenuation and dispersion using short time
Fourier transform.
Ultrasonics 43 (2005) 375–381
with the following values for parameters of the curve (14):
α0 = 1,02 dB⋅cm-1⋅MHz-1,
a = 0,72 dB⋅cm-1.
This preliminary result is consistent with literature values
[8].
Conclusions
Described water-tank-based experimental apparatus is an
useful device for the characterization of soft-solids and, in
particular, ultrasound tissue mimicking materials.
Further tests on the complete measurements system will be
performed by means of a calibrated silicon oil cells, supplied
by National Physical Laboratory (NPL). The final
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