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1

Foundation of the new method of numerical calculations of the nonlinear acoustics fields

Wojcik J., Filipczyński L., Nowicki A.

Hydroacoustics

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2013

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Vol. 16

253--262

EN

We explain, motivation behind this work and briefly describe foundation of new method which we have developed for efficient solution in PC environment of the nonlinear propagation equation with the boundary conditions applied for both circular and not circular transducers (like array). Comparison between new and old method will be presented for strongly nonlinear disturbance. At the end we will demonstrate the results of the numerical calculations of the nonlinear field propagating from the array.

2

Foundation of the new method of numerical calculations of the nonlinear acoustics fields

Wójcik J., Filipczyński L., Kujawska T., Nowicki A.

Hydroacoustics

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2004

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Vol. 7

227-234

EN

We explain, motivation behind this work and briefly describe foundation of new method which we have developed for efficient solution in PC environment of the nonlinear propagation equation with the boundary conditions applied for both circular and not circular transducers (like array). Comparison between new and old method will be presented for strongly nonlinear disturbance. At the end we will demonstrate the results of the numerical calculations of the nonlinear field propagating from the array.

3

Estimation of heat distribution in the acoustic lens of an ultrasonic microscope with the carrier frequency of 1 GHz

Filipczyński L.

Archives of Acoustics

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2004

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Vol. 29, no. 3

427-433

EN

The propagation of heat was analyzed in the lens of an acoustic microscope used for testing of living cells at the frequency of 1~GHz. Information concerning the propagation of heat is necessary for determination of thermal boundary conditions which influence the temperature increase in the tested samples representing acoustical properties of water. The time of temperature propagation from water, heated due to high absorption, to the sapphire body of the lens was estimated to be 0.77 ms. To carry out these calculations the derivations of Carslow and Jaeger [2] and of Tautz [6] were adjusted. On the other hand the propagation time of the acoustic wave in the sapphire body equalled 0.0093 žs only. The time of image formation in the microscope is rather long being equal from one to several seconds due to mechanical inertia of the support vibrating together with the tested sample. The heat capacities of the water volume and the sapphire body were found to be comparable. However, if the heat capacity of the water volume would be many time smaller then the time of the finally attained temperature would be elongated. This effect can be neglected since the time of image formation is 3 orders of magnitude longer than the time of penetration of the sapphire body by the heat supplied by water. As the result a temperature equilibrium will be obtained with the average boundary temperature of water. In such a case no heat flux will penetrate the boundary water - sapphire and the condition of the thermal insulation at the boundary will be fulfilled. This thermal boundary condition makes it possible to determine the real temperature increase in biological specimens.

4

Nonlinear equations of acoustics - numerical solutions and their visualization

Wójcik J., Lewin P. A., Nowicki A., Filipczyński L., Kujawska T., Radulescu E.

Hydroacoustics

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2003

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Vol. 6

137--142

EN

The novel effective numeric solver of the nonlinear scalar wave equation describing the acoustic wave propagation in the attenuating media was derived. The solver was developed for the PC environment. The standard computation data include al! stationary and dynamic characteristics of the radiated ultrasonic pressure field, especially its 4D (space/time) visualization. The results obtained with the solver can be used as the supporting tools (tool) in designing and developments of the multielement linear and phase array transducers applied in ultrasonography.

5

Nonlinear and linear pressure determination in a two-layer structure: solid crystal - water at GHz frequencies

Filipczyński L., Wójcik J., Kujawska T.

Hydroacoustics

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2003

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Vol. 6

143--150

EN

Determination of acoustic pressures at the frequency of 1 GHz by means of PVDF hydrophones is not possible due to their limited frequency response. Moreover, the size of their active electrodes is by about 3 orders of magnitude greater than the resolution in the acoustic microscopes at such a high frequency. Therefore the authors solved this problem at first in a microscope with the working frequency of 34 MHz using both the numerical and experimental methods. A numerical procedure of nonlinear propagation and transducer power measurements were applied giving in effect the same quantitative results. Therefore the identical numerical procedure was used for the l GHz microscope working in the reflection mode. Many pressure field quantities of the microscope were shown, e.g. the pressure values, distributions of the first, second, third and fourth pressure harmonics in and outside of the focus, pulse distortions and their spectra, the resolutions achieved etc. The obtained information on nonlinear propagation effects in microscopy was previously lacking.

6

Nonlinear effects and possible temperature increases in ultrasonic microscopy

Wójcik J., Litniewski J., Filipczyński L., Kujawska T.

Archives of Acoustics

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2002

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Vol. 27, no. 3

191-201

EN

Visualisation of living tissues or cells at a microscopic resolution provides a foundation for many new medical and biological applications. Propagation of waves in ultrasonic microscopy is a complex problem due to finite amplitude distortions. Therefore, to describe it quantitatively, a numerical model developed by the first author was applied. The scanning acoustic microscope operating at 34 MHz was used with strongly focused ultrasonic pulses of 4 periods. For measurements of signals, a 100 MHz PVDF probe was constructed. Its frequency characteristic was found experimentally. The numerical calculation procedure for nonlinear propagation was based on previous papers of the authors. Computations have shown that in the case under consideration, only the spectrum with an input lens pressure amplitude of 1 MPa was in agreement with the experimental one. Based on transducer power measurements, a slightly smaller pressure value was obtained thus confirming, to a good approximation, the correctness of the applied methods. A significant parameter is the ratio of the amplitudes of the second to the first calculated harmonics, which shows the extent of the nonlinearity. In our case it was equal to 0.5. After averaging over the surface of the finite electrode size used in measurements, this ratio was reduced to 0.2. Pressure distributions in the lens cavity and the following region in water were computed for the first 4 harmonics making it possible to determine many features of the nonlinear propagation effects in the microscope. Using the thermal conductivity equation and the rate of heat generation per unit volume, determined for nonlinear propagation in water, a focal temperature increase of 3.3o C was obtained. It was computed for a repetition frequency of 100 kHz. The computed temperature increases can be significant and also harmful, especially when imaging small superficial structures and testing living cell cultures. However, they can be easily decreased by reducing the repetition frequency of the microscope. The developed numerical procedure can be applied for much higher frequencies when living cells in culture are being investigated.

7

Fale krawędziowe przetworników piezoelektrycznych w świetle problematyki pomiarowej

Filipczyński L., Kujawska T.

Prace Naukowe Instytutu Telekomunikacji i Akustyki Politechniki Wrocławskiej. Konferencje

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2001

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Vol. 83, nr 27

393-398

EN

Measurements in the very near field of piezoelectric transducers are fundamental for many ultrasonic problems. In such cases also the transducer vibrations should be known to perform mathematical models of the radiated beams. Acoustical pressure measurements near to the transducer surface can give the necessary information. The pressure of the radiated wave at the transducer surface corresponds to its normal vibration velocity multiplied by the pc value of the medium. However, this is valid only for the central wave, when the edge wave of the transducer can be ignored. On the other hand the pressure measurements on and very near to the transducer surface are not possible because of the voltage leakage between the electronic transmitter and the PVDF hydrophone used in measurements. By means of the numerical model the central and edge waves were found for a plane PZT transducer 7.5 mm in radius, supplied with a 3 MHz voltage pulse composed of 3.5 cycles. Hence practical conditions were elaborated which make it possible to carry out pressure measurements corresponding to vibration velocities of the piezoelectric transducer under consideration.

8

Nonlinear effects computed in Gaussian beams propagating in liquids

Wójcik W., Kujawska T., Filipczyński L.

Hydroacoustics

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2001

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Vol. 4

257--260

EN

The existing theory of focused Gaussian nonlinear beams is based on the parabolic approximation which is not valid near to the sound source, and is restricted to weakly concave transducers. The authors have solved the exact problem of nonlinear propagation of focused Gaussian beams in lossy media without the above limitations. For this purpose a numerical model of the first author was used.

9

Numerical and experimental pressure determination in the very near field of a piezoelectric transducer

Filipczyński L., Kujawska T., Wójcik J., Tymkiewicz R.

Archives of Acoustics

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2001

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Vol. 26, no. 3

223-233

EN

Measurements in the very near field of piezoelectric transducers are fundamental for many ultrasonic problems. In such cases also the transducer vibrations should be known to perform mathematical models of radiated beams. Acoustic pressure measurements near to the transducer surface can give the necessary information. The pressure of the radiated wave at the transducer surface corresponds to its normal vibration velocity multiplied by the ?c value of the medium. However, this is valid only for the central wave, when the edge wave of the transducer can be ignored. On the other hand, pressure measurements on and very near to the transducer surface are not possible because of the voltage leakage between the electronic transmitter and the PVDF hydrophone used in such measurements. By means of a numerical model, central and edge waves were found for a plane PZT transducer 7.5mm in radius, with the applied 2.7MHz voltage pulse composed of 3 cycles. Two types of boundary conditions of Dirichlet and Neumann were considered showing a negligible difference in the case of short pulses. Basing on numerical and experimental results, practical conditions were determined which make it possible to carry out pressure measurements in the very near field of the transducer, and hence to determine the transducer vibrations which are important for modeling ultrasonic pulse beams.

10

Ilościowa ocena nieliniowej propagacji w wodzie i w tkance

Filipczyński L., Kujawska T., Tymkiewicz R., Wójcik J.

Hydroacoustics

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2000

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Vol. 3

53--56

EN

Nonlinear propagation effects were investigated numerically and experimentally u wate r and In blood from the point of view of ultrasonic diagnostic applications in cardlology. Pressure distributions of short and long pulses with the frequency of 3 and 3.5 MHz, radiated by a typical cardiological probe, were found along the ultrasonic beam axis. The numerial results were obtained by means of the numerical code Wf developed previously. The experimental pressure distributions were measured by memu of a membrane PYDF hydrophone. The obtained numerical and experimental results show ing the distributions of the 2-nd and I -st harmonics have shown good agreement allowing us to determine some diagnostic conclusions.

11

Computing and measuring nonlinear and linear propagation by two independent methods

Filipczyński L., Kujawska T., Secomski W., Tymkiewicz R., Wójcik J.

Archives of Acoustics

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1999

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Vol. 24, no. 3

269-288

EN

Nonlinear effects, caused by propagation of ultrasonic pulses with finite amplitudes, were computed and measured in water in the case of pulses with pressures up to 1.5MPapp used in diagnostic devices. An electronic transmitter generated high (280Vpp) and low (47Vpp) voltages, applied to a plane PZT transducer causing in this way nonlinear and linear propagation effects. The carrier frequency of the pulse was 2MHz, while its time duration was 2.5\,ms. The measurements were carried out by means of a typical calibrated PVDF membrane hydrophone and by an electromagnetic (EM) hydrophone, prepared for this study. The pulse measurements by means of the PVDF hydrophone showed a higher number of spectral components than those by means of the EM hydrophone. This effect was explained by sensitivity characteristics that increased in the PVDF and decreased in the EM hydrophone as a function of frequency. Previously, it was shown that the effective frequency band used in measurements by means of the PVDF hydrophone is situated below the resonance, on the increasing slope of the resonanse curve. The properties of the EM hydrophone were analysed on the basis of the plane wave assumption. A procedure was developed to correct distortions of the pulse spectrum and its pressure measured by PVDF and EM hydrophones. In the first case the maximum peak-to-peak pulse pressure should be decreased by 27%, while in the second case it should be increased by only 0.7%, and by 3% if an additional amplifier was used. The sensitivities of PVDF and EM hydrohones were very different and equal for the frequency of 2MHz to 28mV/MPa and 0.10mV/MPa, respectively. The calibration of the EM hydrophone was carried out by means of only two simple: electrical and magnetic independent measurements, although in the EM hydrophone there occured external interferring signals. For the theoretic-numerical detemination of the acoustic fields and their spectra generated in the case of nonlinear and linear propagation the numerical procedure called the WJ Code was applied. It was developed recently by the last-named author of this paper. In calculations absorption in water was taken into account. The critical distance, where distortions caused by nonlinear propagation in water were maximum, was determined by a number of computations of the ultrasonic field as a function of the distance from the transducer. A good agreement between computed results and those measured by two different methods, showing the pulse pressure distribution along the whole beam axis, was confirmed. In this case it was shown that the ?/4 matching layer covering the transducer surface influenced the edge wave radiated by the transducer.

12

Acoustical distortions in capacitance hydrophones and the effect of diaphragms in measurements of shock wave pulses

Filipczyński L., Etienne J., Kujawska T., Wójcik J., Zienkiewicz B.

Archives of Acoustics

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1998

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Vol. 23, no. 2

251-266

EN

The shock wave pulse measured by means of a membrane PVDF hydrophone was compared with the pulse obtained by means of the capacitance hydrophone showing distortions in the pulse trailing edge. The mechanism of distortions in the capacitance hydrophone was explained and confirmed by experiments as caused by transverse waves generated on the surface of the hydrophone's metal plate by compressional incident waves. The effect of the rise time of the measured shock wave pulses was interpreted and analysed by means of diaphragms with various apertures. Interaction of the applied diaphragms with the measured acoustic fields was explained showing their equivalence to the high pass filtering. The differentiating circuit used for determination of the particle velocity from the displacement, measured by the capacitance hydrophone, was analysed. Also an improved capacitance hydrophone was applied in measurements.

13

A multilayer method for linearity determination of the PVDF hydrophone for pressures up to 2.3MPa

Filipczyński L., Etienne J., Kujawska T., Tymkiewicz R., Wójcik J.

Archives of Acoustics

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1998

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Vol. 23, no. 4

513-520

EN

A new method of linearity measurements of a PVDF membrane hydrophone was elaborated. High pressure pulses up to 6MPa were obtained in the focus of a concave PZT transducer with the frequency of 3MHz. The method is based on the pressure decrease of these pulses transmitted through metal layers with known acoustic impedances, immersed in water. In this way one obtained pressure changes at constant shapes (spectrum) of the pulses which were measured by means of the hydropbone under investigation. The measurement results confirmed the linearity of the hydrophone up to pressures equal to 2.3MPa. Correlation coefficients of 5 measured relations were in average equal to r=0.994.

14

Possible temperature increases in soft tissues in the case of nonlinear and linear wave propagation

Filipczyński L., Kujawska T., Tymkiewicz R., Wójcik J.

Hydroacoustics

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1997

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Vol. 1

329--332

EN

It is well known that the nonlinear propagation increases the absorption of acoustic waves in the medium thus increasing the temperature effects. According to the recently developed new theoretical approach it is possible to determine in a simple way the effective absorption in the case of nonlinear propagation basing on the pulse spectrum analysis [Wójcik, 1996]. In this way it was possible to find the corresponding absorption values occuring in ultrasonography. In this case a classical PVDF membrane hydrophone was used to demonstrate and to measure nonlinear effects. Analysing the obtained wave spectra it was possible to determine the increase of the effective tissue absorption and hence to find the rate of heat generation per unit volume which is crucial for temperature elevations In this way possible temperature increases for the case of nonlinear and linear propagation can be determined.