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1 Figure# Determination of B/A of Biological Media by Measuring and Modeling Nonlinear Distortion of Pulsed Acoustic Wave in Two-Layer System of Media

Abstract

Knowledge of the acoustic nonlinearity parameter, B/A, of biological fluids or soft tissues is necessary whenever high intensity pressure fields are induced. A numerical model
recently developed in our lab is capable of fast predicting the nonlinear distortion of pulsed finite-amplitude acoustic waves
generated from axisymmetric sources propagating through multilayer attenuating media. Quantitative analysis of the obtained
results enabled developing the alternative method for determination of the B/A of biological media. First, the method involves measuring the nonlinear waveform distortion of the tone burst propagating
through water. Then, it involves numerical modeling (in frequency domain) using the Time-Averaged Wave Envelope (TAWE) approach.
The numerical simulation results are fitted to the experimental data by adjusting the source boundary conditions to determine
accurately the source pressure, effective radius and apodization function being the input parameters to the numerical solver.
Next, the method involves measuring the nonlinear distortion of idem tone burst passing through the two-layer system of parallel
media. Then, we numerically model nonlinear distortion in two-layer system of media in frequency domain under experimental
boundary conditions. The numerical simulation results are fitted to the experimental data by adjusting the B/A value of the tested material. Values of the B/A for 1.3-butanediol at both the ambient (25°C) and physiological (36.6°C) temperatures were determined. The obtained result (B/A = 10.5 ± 5% at 25°C) is in a good agreement with that available in literature. The B/A = 11.5 ± 5% at 36.6°C was determined.
KeywordsNonlinearity parameter measurement-
B/A
-Nonlinear propagation-Biological media-PVDF membrane hydrophone

Determination of B/A of Biological Media

by Measuring and Modeling Nonlinear

Distortion of Pulsed Acoustic Wave

in Two-Layer System of Media

T. Kujawska, J. Wójcik, and A. Nowicki

Abstract Knowledge of the acoustic nonlinearity parameter, B/A, of biological

ﬂuids or soft tissues is necessary whenever high intensity pressure ﬁelds are

induced. A numerical model recently developed in our lab is capable of fast

predicting the nonlinear distortion of pulsed ﬁnite-amplitude acoustic waves gener-

ated from axisymmetric sources propagating through multilayer attenuating media.

Quantitative analysis of the obtained results enabled developing the alternative

method for determination of the B/A of biological media. First, the method involves

measuring the nonlinear waveform distortion of the tone burst propagating through

water. Then, it involves numerical modeling (in frequency domain) using the Time-

Averaged Wave Envelope (TAWE) approach. The numerical simulation results are

ﬁtted to the experimental data by adjusting the source boundary conditions to deter-

mine accurately the source pressure, effective radius and apodization function being

the input parameters to the numerical solver. Next, the method involves measuring

the nonlinear distortion of idem tone burst passing through the two-layer system of

parallel media. Then, we numerically model nonlinear distortion in two-layer sys-

tem of media in frequency domain under experimental boundary conditions. The

numerical simulation results are ﬁtted to the experimental data by adjusting the B/A

value of the tested material. Values of the B/A for 1.3-butanediol at both the ambi-

ent (25◦C) and physiological (36.6◦C) temperatures were determined. The obtained

result (B/A =10.5 ±5% at 25◦C) is in a good agreement with that available in

literature. The B/A =11.5 ±5% at 36.6◦C was determined.

Keywords Nonlinearity parameter measurement ·B/A ·Nonlinear propagation ·

Biological media ·PVDF membrane hydrophone

1 Introduction

Nonlinear effects incidental to the ﬁnite-amplitude acoustic wave propagation in

thermo-viscous ﬂuids are systematically studied theoretically and experimentally

in many laboratories around the world because of extensive possibilities of their

T. Ku ja ws ka (B)

Institute of Fundamental Technological Research Polish Academy of Sciences,

Warsaw 00-049, Poland

295

M.P. André et al. (eds.), Acoustical Imaging, Acoustical Imaging 30,

DOI 10.1007/978-90-481-3255-3_34, C

Springer Science+Business Media B.V. 2011

296 T. Kujawska et al.

practical applications, especially for medical purposes. Knowledge of the B/A of

media through which the acoustic wave propagates is indispensable for predicting

nonlinear pressure ﬁelds in order to assess safety of modern US medical equipments

or to improve image quality using the Tissue Harmonic Imaging (THI) tech-

nique. The therapeutic ultrasound techniques, such as the High Intensity Focused

Ultrasound (HIFU) or lithotripsy, also produce the nonlinear waveform distortion

leading to enhanced local heating or thermal ablation of tissues at the focal region.

The purpose of this work was to develop an alternative, relatively simple in use

method for determining the nonlinearity parameter, B/A, of biological liquids or

soft tissues. The proposed method is based on the comparison of the simulated

numerically (in frequency domain under experimental boundary conditions) non-

linear waveform distortion of the pulsed acoustic wave propagating through the

two-layer system of parallel media: water–tested material with the measured one.

Water is used as the reference medium with known nonlinear properties in order

to calibrate the experimental setup. The numerical model used accounts for the

effects of absorption, diffraction, nonlinear interactions of harmonics as well as for

the reﬂection and transmission at the media interfaces. The source boundary condi-

tion parameters such as the pressure on the surface, effective radius, initial acoustic

pulse pressure-time waveform, radiating aperture apodization function as well as

the tested material linear parameters such as density, sound velocity, frequency-

dependent attenuation law are introduced as input data to the numerical model after

their preliminary measuring.

2 Numerical Model

The numerical model used for describing the nonlinear waveform distortion of the

pulsed ﬁnite-amplitude sound wave propagating through a nonlinear lossy medium

accounts for the effects of diffraction, absorption and nonlinear interactions of

harmonics and is comprehensively described in Reference [1]. The model was

made computationally efﬁcient by means of replacing the Fourier–series solution

approach by the Time-Averaged Wave Envelope (TAWE) algorithm. The computer

implementation of the numerical model for axisymmetric cases in a form of the 3D

numerical solver, capable of predicting pulsed nonlinear acoustic ﬁelds from plane

or focused circular acoustic sources in a multilayer system of parallel media with

arbitrary attenuation law, was the powerful research instrument for studying prop-

erties of the nonlinear acoustic ﬁelds produced in various biological media from

various ultrasonic transducers.

3 Methods and Materials

The degree of nonlinear waveform distortion of the pulsed ﬁnite-amplitude wave

generated from the acoustic source and propagating through the attenuating medium

depends on the nonlinear properties of this medium as well as on the source

operating parameters. The source parameters required for the numerical model

B/A from Nonlinear Distortion of Pulsed Wave in Two-Layer Media 297

include the pressure amplitude on the surface, effective radius, focal length, fre-

quency, initial pulse waveform and apodization function. The medium parameters

required for the numerical model include density, sound velocity, absorption coef-

ﬁcient, its frequency-dependent power-law and nonlinearity parameter, B/A.If

boundary condition parameters of the source and linear parameters of the medium

are determined experimentally then the B/A of the medium can be determined

by ﬁtting the calculated axial pressure variation of the fundamental and ﬁrst two

harmonics of the propagating tone burst to the measured one. The principle of

measuring the nonlinearity parameter, B/A, of the medium being examined involves:

1. Determining the linear parameters of the medium being examined by mea-

suring its density, ρ, sound velocity, c, small-signal attenuation coefﬁcient, α,

attenuation coefﬁcient frequency-dependence law α(f) at chosen temperature T;

2. Determining the transducer boundary condition parameters: effective radius a,

pressure amplitude P0at the surface, initial pressure-time waveform of the acous-

tic pulse and radiating aperture apodization function by measuring the axial and

radial distributions of both the peak- to-peak and harmonics pressure amplitudes

in water and ﬁtting the numerically simulated results to the experimental data

by adjusting the source boundary conditions parameters. This preliminary mea-

surements calibrate the experimental setup and determines an accuracy of the

proposed method;

3. Measuring nonlinear waveform distortion of the tone burst propagating through

the two-layer system of parallel media: water–tested material using the method

of the ﬁxed path-length through the water layer and the variable path-length

through the layer of the tested material [2,3];

4. Introducing the input parameters into the numerical model and ﬁtting the the-

oretical results obtained for the two-layer system of media to the experimental

data by adjusting the B/A value of the tested material.

3.1 Experimental setup

The experimental set-up used for the measurements is shown in Fig. 1.

The measurements were carried out at both the 25◦C and 36.6◦C tempera-

tures with the 16 mm diameter, 2.2 MHz central frequency, focused (focal length

F=100 mm) piezoceramic (Pz27 Ferroperm, Norway) transducer immersed

in temperature-controlled distilled degassed water. The transducer had a quarter-

wavelength matching layer, was back-loaded and positioned on the translation stage

driven by computer-controlled stepper motors allowing its motion in horizontal

and vertical planes with varied steps (from 0.1 to 5 mm). The output signals were

recorded by the broadband (calibrated up to 40 MHz) bi-laminar polyvinylidene

diﬂuoride (PVDF) membrane hydrophone (Sonora Medical, Inc. S/N S5-153, P-159

preampliﬁer) with the 0.414 mm diameter of the active element. The hydrophone

was immersed in water and ﬁxed on the acoustic axis. To maximise the signal to

noise ratio at the measurement of the 18th harmonic the transducer were driven

by 8-cycle tone bursts from an Arbitrary Function Generator (Ritec Advanced

Measurement System RAM-10000, Warwick, RI, USA). The amplitude of the

298 T. Kujawska et al.

Fig. 1 Schematic diagram of the experimental setup

excitation voltage, frequency and duration of the tone bursts were controlled by PC.

Nonlinear ﬁelds were produced when excitation level at the output of the generator

was 178.9 Vpp. (producing source pressure of 0.225 MPa). The hydrophone output

was additionally ampliﬁed by 20 dB using the linear broadband ampliﬁer (Ritec

BR-640, Warwick, RI, USA) and then fed to the input of an 8-bit digital oscillo-

scope (HP54503A, Hewlett Packard, Colorado Springs, CO, USA) with a 500 MHz

sampling frequency. The received signals were digitised and averaged over 16 con-

secutive waveforms in the oscilloscope memory and then transferred for spectral

analysis to PC. The amplitude of the measured harmonic components was corrected

for the hydrophone sensitivity dependence on frequency.

3.2 Methodology of Measurements

Initially, the preliminary measurements are carried out in water in order to determine

the acoustic axis as well as the input data to the numerical model. The acoustic axis

was accurately determined from symmetry of the acoustic beam patterns that were

B/A from Nonlinear Distortion of Pulsed Wave in Two-Layer Media 299

visualized as isobar contour lines. The input data included the acoustic parameters of

water: density, ρ, sound velocity, c, attenuation coefﬁcient, α1, frequency-dependent

attenuation law, α(f)=α1·f2, nonlinearity parameter, B/A, as well as the transducer

boundary condition parameters: effective radius, a, focal length, F, source pressure

P0, pressure-time waveform, P(t), of the initial tone burst that best reproduced the

tone burst measured on the acoustic axis close to the transducer surface, radiating

aperture apodization function, g(r), which produced the radial pressure distribution

close to the transducer that best reproduced this measured.

The apodization function, source pressure and pressure-time waveform of the

initial tone burst as the input data to the numerical solver were determined at

lower excitation level by measuring the radial and axial pressure distributions

and pressure-time waveform of the tone burst close to the radiating surface (at

5÷15 mm axial distance). The pulse waveforms measured along the acoustic

axis were processed by the FFT technique, corrected for the hydrophone frequency-

dependent sensitivity characteristic and then the axial variation of the fundamental

and ﬁrst two harmonics were compared with those numerically simulated by the 3D

numerical solver while keeping both the effective radius and apodization function

constant and varying the source pressure. The best agreement between calculation

and measurement results determined the value of the source pressure.

Figure 2illustrates very good agreement between the calculated results and

experimental data in water for the source considered which produced 0.225 MPa

pressure on the surface. Degree of these results agreement, determined by the ratio

of the fundamental to the 2nd or 3rd harmonics amplitude as a function of the axial

distance from the transducer face, was equal to 0.96 ±0.034 for all points measured.

These results validated correctness and accuracy of the numerical model proposed

and calibrated the experimental setup.

To measure nonlinear waveform distortion of the tone burst propagating through

the two-layer system of parallel media: water–tested material the method of ﬁxed

0 102030405060708090100110120

0

0.5

1

1.5

.

Axial range z (mm)

P/P 0

1st

2nd

3rd

Fig. 2 Axial pressure

variation of the fundamental

(1st), 2nd and 3rd harmonics

for the 8-cycle tone burst

propagating in water.

Fundamental frequency

2.2 MHz, source pressure

0.225 MPa. Experiment

(points), theory (solid lines)

300 T. Kujawska et al.

path-length in water and variable path-length in the tested material was used.

In previous publications [4,5] the speciﬁc feature of pulsed nonlinear ﬁelds in

water, generated from circular sources of chosen dimensions and frequency, was

proved. Namely, the distance from the source at which the rapid increase of ampli-

tude of the 2nd harmonics (in the spectrum of the propagating tone burst) begins

is speciﬁc for this source and does not dependent on the source pressure. This

characteristic property of the nonlinear ﬁelds in water was used to develop an alter-

native method for determination of the nonlinearity parameter B/A of biological

media.

The main principle of the proposed method is based on predicting numerically

nonlinear waveform distortion (in frequency domain and under experimental bound-

ary conditions) for the tone burst propagating through the two-layer system of

parallel media: water–tested material and then ﬁtting the obtained numerical simula-

tion results to the experimental data by adjusting the B/A of the tested medium. For

each source with chosen dimensions and central frequency the thickness of water

layer in the two-layer system of media is speciﬁc and equal to the axial distance

from the source at which a rapid increase of the 2nd harmonics and appearance

of the 3rd harmonics for the tone burst propagating in water occurs. For the trans-

ducer considered here this distance was found to be 4 cm (see Fig. 2). Thickness

of the tested medium layer may be chosen arbitrarily, however, soft tissues are

highly attenuating media, and thus thickness of 1.3-butanediol layer was chosen

to be 9 cm.

To determine experimentally nonlinear waveform distortion of the tone burst

propagating through the two-layer system of media: water–tested material the

method of a ﬁxed path-length through the water layer and variable path-length

through the tested material layer was used. In practice this requirements were

fulﬁlled by enclosing water in a ﬁxed-length chamber and tested ﬂuid in a variable-

length chamber. The design of the chambers was based on two coaxially mounted

plastic pipes with different diameter and acoustically transparent polyethylene win-

dow at the output end. The smaller pipe was ﬁxed coaxially with the transmitting

probe and ensured the position of the transducer face at the desired distance from

its output window and in parallel with it. The larger pipe was connected with the

smaller one by a reduction rubber sleeve and ﬁxed to the water tank. The output

window of the larger pipe was mounted in parallel with the membrane of the PVDF

hydrophone. Although the larger pipe had only one degree of freedom the trans-

ducer and hydrophone had tree degrees of freedom that allowed us to minimize

alignment problems. Figure 1illustrates the experimental setup for generating and

recording nonlinear waveform distortion of the tone burst propagating through the

two-layer system of ﬂuids. The axial movement of the transducer to the hydrophone

with the step of 0.1 mm was achieved using the translation stage controlled by a PC

via GPIB bus interface. The tested ﬂuid path-length was varying from 4 to 9 cm.

The outer tank was ﬁlled with tap water. To provide the temperature control in

the inner tank ﬁlled with distilled water the immersion heating circulator (Julabo

B/A from Nonlinear Distortion of Pulsed Wave in Two-Layer Media 301

ME-6, Labortechnik GmbH, Germany) was mounted on the wall of the outer tank.

The distorted electric signals were recorded by hydrophone, sampled and processed

by the FFT. The amplitudes of obtained harmonics were corrected accordingly to

the hydrophone frequency-dependent sensitivity characteristic (V/μPa) and ﬁtted

to those numerically predicted by adjusting the B/A value of the tested material.

The numerical simulation results best ﬁtted to the measured data determined the

nonlinearity parameter of the medium under examination.

4 Results

The 1.3-butanediol (99%, Sigma-Aldrich Chemie GmbH, Steinheim, Germany) was

considered as the tested material. Two different values of the B/A of this medium

was determined by two different authors which used two different methods. The

value measured by Chavrier, et al., (B/A=11) [6] is different from the value

estimated by Granz (B/A=7.3) [7]. Our measurements were done at both the

25◦C and 36.6◦C temperatures. The acoustic parameters of water and 1.3-butanediol

assumed for calculations are quoted in Table 1. They were available from literature

for water at both temperatures and for 1.3-butanediol at 25◦C. They were measured

at 36.6◦C.

Numerical simulations were made for the B/A of tested material varying from 7

to 11 with a step of 0.5. The axial variation of the fundamental (1st), 2nd and 3rd har-

monics calculated for the 8-cycle tone burst generated from the source considered

and propagating through the two-layer system of media including 4 cm of water and

9 cm of 1.3-butanediol is presented in Fig. 3for the axial range from 8 to 13 cm.

In this case both the measured and calculated ratio of the 1st/2nd and 1st /3rd har-

monics versus the axial range corresponding to the tested material layer are shown

in Fig. 4.

The best correlation coefﬁcient (0.986) between measured and calculated results

for 1.3-butanediol was obtained for the value of the B/A=10.5 at 25◦C and B/A=

11.5 at 36.6◦C. The proposed method allows us to get results with a reasonable

degree of accuracy, ±5%.

Table 1 Acoustic parameters of water and 1.3-butanediol at 25◦C and 36.6◦C

Material

Temperature

(◦C)

Density

(kg/m3)

Sound

velocity

(m/s)

Attenuation

coefﬁcient

(Np/m ·Hz2)B/A

Distilled water 25 1,000 1,497 2.8 ·10−14 5.2

Distilled water 36.6 1,000 1,524 2 ·10−14 5.5

1.3-butanediol 25 1,005 1,530 127 ·10−14 7÷11

1.3-butanediol 36.6 1,005 1,560 95 ·10−14 7÷11

302 T. Kujawska et al.

345678910111213

0

0.1

0.2

0.3

.

(B/A) bd = 7

(B/A)w = 5.2

(B/A) bd = 11

2nd

Axial range (cm)

P/P0

P/P0

345678910111213

0

0.05

0.1

0.15

.

3rd

Axial range (cm)

(B/A)w = 5.2

(B/A)bd = 11

(B/A) bd = 7

Fig. 3 Calculated axial variation of the second (2nd) and third (3rd ) harmonics for the 8-cycle tone

burst propagating through water (thick lines) and through the two-layer system of 4 cm of water

+9 cm of 1.3-butanediol for (B/A)bd varying from 7 to 11 with a step of 1

80 90 100 110 120130

0

10

20

30

40

50

.

Axial range (cm)

1bd / 3bd

80 90 100 110 120 130

2

3

4

5

6

7

8

.

.

Axial range (cm)

(B/A )bd = 11

(B/A )bd = 11

1bd / 2bd

(B/A )bd = 7

(B/A )bd = 7

1w / 2w

1w / 3w

Fig. 4 Axial variation of the ratio of the 1st to 2nd and 1st to 3rd harmonics for the 8-cycle tone

burst propagating through water (with index w) or through two-layer system including 4 cm of

water +9 cm of 1.3-butanediol for (B/A)bd varying from 7 to 11 with a step of 1. Experiment

(points) and calculation (lines) results

B/A from Nonlinear Distortion of Pulsed Wave in Two-Layer Media 303

Acknowledgements This work was supported in part by the Ministry of Science and Higher

Education (Grant Nr N N518 402734).

References

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329 (2006)

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dence of attenuation coefﬁcient and velocity in amniotic ﬂuid, urine and human serum albumin

solutions. Ultrasound Med. Biol. 31(10), 1375–1381 (2005)

3. Verma, P.K., Humphrey, V.F., Duck, F.A.: Broadband attenuation and nonlinear propagation in

biological ﬂuids: An experimental facility and measurements. Ultrasound Med. Biol. 31(12),

1723–1733 (2005)

4. Kujawska, T., Wójcik, J.: Harmonic ultrasound beams forming by means of radiating source

parameters. Hydroacoustics 7, 135–142 (2004)

5. Kujawska, T.: A new method for determination of the acoustic nonlinearity parameter B/A

in multilayer biological media. Proceedings of the 5th World Congress on Ultrasound, Paris,

81–84 (2003)

6. Chavrier, F., Lafon, C., Birer, A., Barriere, C., Jacob, X., Cathignol, D.: Determination of the

nonlinear parameter by propagating and modelling ﬁnite amplitude plane waves. J. Acoust.

Soc. Am. 119(5), 2639–2644 (2006)

7. Grantz, B.: Measurement of shock wave properties after the passage through a tissue-mimicking

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- CitationsCitations8
- ReferencesReferences12

- The distance z 1 was determined theoretically (using nonlinear propagation model in water) as the axial distance from the transducer used at which the amplitude of the second harmonic component starts to be discernible. As shown in previous publications this distance is independent on the source pressure level providing formation of weak or moderate nonlinear beams [4,5,6]. In order to predict both, the pressure and heat sources distributions produced in the two-layer system of media by the pulsed focused nonlinear acoustic beam the several boundary condition parameters characterizing both the source and media are required.

[Show abstract] [Hide abstract]**ABSTRACT:**A tissue thermal conductivity (Ks) is an important parameter which knowledge is essential whenever thermal fields induced in selected organs are predicted. The main objective of this study was to develop an alternative ultrasonic method for determining Ks of tissues in vitro suitable for living tissues. First, the method involves measuring of temperature-time T(t) rises induced in a tested tissue sample by a pulsed focused ultrasound with measured acoustic properties using thermocouples located on the acoustic beam axis. Measurements were performed for 20-cycle tone bursts with a 2 MHz frequency, 0.2 duty-cycle and 3 different initial pressures corresponding to average acoustic powers equal to 0.7 W, 1.4 W and 2.1 W generated from a circular focused transducer with a diameter of 15 mm and f-number of 1.7 in a two-layer system of media: water/beef liver. Measurement results allowed to determine position of maximum heating located inside the beef liver. It was found that this position is at the same axial distance from the source as the maximum peak-peak pressure calculated for each nonlinear beam produced in the two-layer system of media. Then, the method involves modeling of T(t) at the point of maximum heating and fitting it to the experimental data by adjusting Ks. The averaged value of Ks determined by the proposed method was found to be 0.5±0.02 W/(m·°C) being in good agreement with values determined by other methods. The proposed method is suitable for determining Ks of some animal tissues in vivo (for example a rat liver).- Recent years have seen a high research interest in various methods based on non-classical nonlinear effects associated with ultrasonic wave propagation. Various methods have been used, for instance, for damage evaluation in metallic structures (mainly by observation generation of higher harmonics, also with Lamb and Rayleigh waves)[12,[49][50][51][52][53][54][55], even of complex shape[22], composites[56], bones[57], soft tissues and biological media[58], concrete[12,59], soil and granular materials[8]and glass[60]. Most of these applications relate to fatigue cracks and fractures.

[Show abstract] [Hide abstract]**ABSTRACT:**The past decades have been marked by a significant increase in research interest in nonlinearities in micro-cracked and cracked solids. As a result, a number of different nonlinear acoustic methods have been developed for damage detection. A general consensus is that – under favourable conditions – nonlinear effects exhibited by cracks are stronger than crack-induced linear phenomena. However, there is still limited understanding of physical mechanisms related to various nonlinearities. This problem remains essential for implementation of nonlinear acoustics for damage-detection applications. This paper reviews modelling approaches used for nonlinear crack–wave interactions. Various models of classical and nonclassical crack-induced elastic, thermo-elastic and dissipative nonlinearities have been discussed.- For the transducer considered here the axial distance at which sudden accretion of the 2nd harmonics amplitude occurs was found to be 60 mm. This characteristic feature of the weak and moderate pulsed nonlinear acoustic beams generated from axially-symmetric sources in water was used to develop an alternative semi-empirical method for determination of the nonlinearity parameter B/A of clinically relevant media (Kujawska et al., 2011aKujawska et al., , 2011c). Good agreement between measurement data and theoretical predictions in water confirmed applicability of the numerical model based on the TAWE method as an effective research tool for predicting of the 3D (2D space + time) pulsed nonlinear acoustic pressure fields produced by circular focused sources in water.Fig. 5. Axial pressure variations of the fundamental (1w) and 2nd (2w) harmonic amplitudes in the pulsed focused nonlinear acoustic beams produced by the transducer used generating in water 8-cycle tone bursts with the initial pressure amplitude of 113 kPa (left) and 37 kPa (right).

[Show abstract] [Hide abstract]**ABSTRACT:**In many therapeutic applications of a pulsed focused ultrasound with various intensities the finite-amplitude acoustic waves propagate in water before penetrating into tissues and their local heating. Water is used as the matching, cooling and harmonics generating medium. In order to design ultrasonic probes for various therapeutic applications based on the local tissue heating induced in selected organs as well as to plan ultrasonic regimes of treatment a knowledge of pressure variations in pulsed focused nonlinear acoustic beams produced in layered media is necessary. The main objective of this work was to verify experimentally the applicability of the recently developed numerical model based on the Time-Averaged Wave Envelope (TAWE) approach (WOJCIK et al., 2006) as an effective research tool for predicting the pulsed focused nonlinear fields produced in two-layer media comprising of water and tested materials (with attenuation arbitrarily dependent on frequency) by clinically relevant axially-symmetric therapeutic sources. First, the model was verified in water as a reference medium with known linear and nonlinear acoustic properties. The measurements in water were carried out at a 25 degrees C temperature using a 2.25 MHz circular focused (f/3.0) transducer with an effective diameter of 29 mm. The measurement results obtained for 8-cycle tone bursts with three different initial pressure amplitudes varied between 37 kPa and 113 kPa were compared with the numerical predictions obtained for the source boundary condition parameters determined experimentally. The comparison of the experimental results with those simulated numerically has shown that the model based on the TAWE approach predicts well both the spatial-peak and spatial-spectral pressure variations in the pulsed focused nonlinear beams produced by the transducer used in water for all excitation levels complying with the condition corresponding to weak or moderate source-pressure levels. Quantitative analysis of the simulated nonlinear beams from circular transducers with ka >> 1 allowed to show that the axial distance at which sudden accretion of the 2nd or higher harmonics amplitude appears is specific for this transducer regardless of the excitation level providing weak to moderate nonlinear fields. For the transducer used, the axial distance at which the 2nd harmonics amplitude suddenly begins to grow was found to be equal to 60 mm. Then, the model was verified experimentally for two-layer parallel media comprising of a 60-mm water layer and a 60-mm layer of 1.3-butanediol (99%, Sigma-Aldrich Chemie GmbH, Steinheim, Germany). This medium was selected because of its tissue-mimicking acoustic properties and known nonlinearity parameter B/A. The measurements of both, the peak- and harmonic-pressure variations in the pulsed nonlinear acoustic beams produced in two-layer media (water/1.3-butanediol) were performed for the same source boundary conditions as in water. The measurement results were compared with those simulated numerically. The good agreement between the measured data and numerical calculations has shown that the model based on the TAWE approach is well suited to predict both the peak and harmonic pressure variations in the pulsed focused nonlinear sound beams produced in layered media by clinically relevant therapeutic sources. Finally, the pulsed focused nonlinear fields from the transducer used in two-layer media: water/castor oil, water/silicone oil (Dow Corning Ltd. , Coventry, UK), water/human brain and water/pig liver were predicted for various values of the nonlinearity parameter of tested media.- The rat stomach area covering liver is located at the specific axial distance z 1 from the transducer face. In a previous publication [2] it was shown that, for circular acoustic sources which are many wavelengths across (ka >>1) and which produce in water weak to moderate nonlinear fields the axial distance z 1 at which sudden growth of the second harmonics occurs is specific for each source and is independent of the source pressure. The weak to moderate nonlinear fields in water mean that the shock formation distance is in the transition or far field regions of the sound beam, i.e. the ratio of the shock formation distance l D to the Rayleigh distance R 0 is larger than 0.3 [3].

[Show abstract] [Hide abstract]**ABSTRACT:**The main aim of this work was numerical modeling of temperature fields induced in soft tissues in vivo by pulsed focused ultrasound during neurodegenerative disease treatment and experimental verification of the proposed model for a rat liver. The new therapeutic approach to neurodegenerative diseases consists of stimulation of enhanced expression of the Heat Shock Proteins (HSP) which are responsible for immunity of cells to stress. During therapy the temperature rise in tissues in vivo should not exceed 6 °C above level of the thermal norm (37 °C). First, the 3D acoustic pressure field, and the rate of heat production per unit volume due to that field, were calculated using our 3D numerical solver capable of predicting nonlinear propagation of pulsed high intensity waves generated from circular focused acoustic sources in multilayer configuration of attenuating media. The two-layer configuration of media (water--rat liver) assumed in calculations fairly well approximated both the real anatomic dimensions of rat liver and the geometric scheme of our experimental set-up. A numerical solution of the Pennes bio-heat transfer equation which accounted for the effects of heat diffusion, blood perfusion and metabolism rates, was employed to calculate the temperature fields induced in the rat liver by the ultrasonic beam. The numerical simulation results were verified experimentally using a thermocouple inserted in the liver of a rat under anesthesia at the beam focus. The quantitative analysis of the obtained results enabled estimation of the effects of several acoustic and thermal parameters of the rat liver in vivo on the temperature rise, as well as determination of exposure time for ultrasonic beams with varied acoustic power generated by a 2-MHz circular transducer of 15-mm diameter and 25-mm focal length, in order to avoid the tissue overheating that leads to cells necrosis, which would be unacceptable in neurodegenerative disease treatment.- This distance was selected as the axial distance at which the 2nd harmonics amplitude – for the tone bursts generated from the transducer used and nonlinearly distorted during propagation in water – started to grow rapidly. As has been shown in previous publications (Kujawska et al., 2009; Kujawska et al., 2011) this distance is specific for each transducer with ka ≫ 1 and does not depend on the pressure amplitude on the source producing weak to moderate nonlinear fields in water. The choice of this distance was done to maximize the harmonics generation effect being one of the reasons of the temperature rise induced in tissues by nonlinear ultrasound.

[Show abstract] [Hide abstract]**ABSTRACT:**Many therapeutic applications of pulsed focused ultrasound are based on heating of detected lesions which may be localized in tissues at different depths under the skin. In order to concentrate the acoustic energy inside tissues at desired depths a new approach using a planar multi-element annular array transducer with an electronically adjusted time-delay of excitation of its elements, was proposed. The 7-elements annular array transducer with 2.4 MHz center operating frequency and 20 mm outer diameter was produced. All its elements (central disc and 6 rings) had the same radiating area. The main purpose of this study was to investigate ther-mal fields induced in bovine liver in vitro by pulsed focused ultrasonic beams with various acoustic properties and electronically steered focal plane generated from the annular array transducer used. The measurements were performed for the radiating beams with the 20 mm focal depth. In order to maximize nonlinear effects introduc-ing the important local temperature rise, the measurements have been performed in two-layer media comprising of a water layer, whose thickness was specific for the transducer used and equal to 13 mm, and the second layer of a bovine liver with a thickness of 20 mm. The thickness of the water layer was determined numerically as the axial distance where the amplitude of the second harmonics started to increase rapidly. The measurements of the temperature rise versus time were performed us-ing a thermocouple placed inside the liver at the focus of the beam. The temperature rise induced in the bovine liver in vitro by beams with the average acoustic power of 1 W, 2 W and 3 W and duty cycle of 1/5, 1/15 and 1/30, respectively, have been mea-sured. For each beam used the exposure time needed for the local tissue heating to the temperature of 43 • C (used in therapies based on ultrasonic enhancement of drug delivery or in therapies involving stimulation of immune system by enhancement of the heat shock proteins expression) and to the temperature of 56 • C (used in HIFU therapies) was determined. Two sets of measurements were done for each beam con-sidered. First, the thermocouple measurement of the temperature rise was done and 938 T. Kujawska et al. next, the real-time monitoring of dynamics of growth of the necrosis area by using ultrasonic imaging technique, while the sample was exposed to the same acoustic beam. It was found that the necrosis area becomes visible in the ultrasonic image only for beams with the average acoustic power of 3 W, although after cutting the sample the thermo ablated area was visible with the naked eye even for the beams with lower acoustic power. The quantitative analysis of the obtained results allowed to determine the exposure time needed to get the necrosis area visible in the ultrasonic image.- Then the focal plane occurs within the tissue sample. In previous publications [2, 3] have been shown that for any circular transducer with ka >>1 and weak to moderate source pressure level the axial distance z 1 at which sudden growth of the second harmonics begins (for the tone burst generated from that transducer in water and propagating there) is specific for that transducer and constant independently on the source pressure amplitude. The weak to moderate source level means that in the nonlinear acoustic field produced by the source in water the ratio of the shock formation distance l D to the Rayleigh distance R 0 is larger than about 0.3 [4].

[Show abstract] [Hide abstract]**ABSTRACT:**Beneficial biological effects in soft tissues can be induced by focused ultrasound of low intensity (LIFU). For example, increasing of cells immunity to stress can be accomplished through the enhanced heat shock proteins (Hsp) expression induced by the low intensity focused ultrasound. The possibility to control the Hsp expression enhancement in soft tissues in vivo can be the potential new therapeutic approach to neurodegenerative diseases that utilizes the known feature of cells to increase their immunity to stresses through the Hsp expression enhancement. The controlling of the Hsp expression enhancement by adjusting the level of exposure to ultrasound energy would allow evaluating of ultrasound-mediated treatment efficiency. Our objective was to develop the numerical model capable of predicting in space and time temperature fields induced in multilayer nonlinear attenuating media by a circular focused transducer generating pulsed acoustic waves and to compare the results calculated for two-layer configuration of media: water -fresh rat liver with the experimental data. The measurements of temperature variations versus time at 5 points on the acoustic beam axis within the tissue sample were performed using 0.2-mm diameter thermocouples. Temperature fields were induced by the transducer with 15-mm diameter, 25-mm focal length and 2-MHz centre frequency generating tone bursts with the intensity I SPTA varied between 0.45 W/cm 2 and 1.7 W/cm 2 and duration varied between 20 and 500 cycles at the same 20-% duty cycle and 20-min exposure time. Quantitative analysis of the obtained results allowed to show that, for example, for the acoustic beam with intensity I SPTA = 1.13 W/cm 2 exposure time to ultrasound should not be longer than 10 min to avoid cells necrosis following the 43-o C temperature threshold exceeding.

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Atherosclerosis risk prediction.
Measurements with 20MHZ US imaging and Doppler

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Thesis (Ph. D.)--University of Washington, 2008. In applications of therapeutic ultrasound such as shock wave lithotripsy (SWL) and high-intensity focused ultrasound (HIFU), cavitation and the associated bubble dynamics play an important role. Moreover, bubble dynamics have not been fully studied in the context of the large acoustic excitations, elevated temperatures, and gas-saturated... [Show full abstract]

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