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Sonodynamic therapy (SDT) is a promising technique based on the ability of certain substances, called sonosensitizers, to sensitize cancer cells to non-thermal effects of low-energy ultrasound waves, allowing their destruction. Sonosensitization is thought to induce cell death by direct physical effects such as cavitation and acoustical streaming as well as by complementary chemical reactions generating oxygen free radicals. One of the promising sonosensitizers is 5-aminolevulinic acid (ALA) which upon selective uptake by cancer cells is metabolized and accumulated as protoporphyrin IX. The objective of the study was to describe ALA-mediated sonodynamic effects in vitro on a rat RG2 glioma cell line. Glioma cells, seeded at the bottom of 96-well plates and incubated with ALA (10 µg/ml) for 6 h, were exposed to the sinusoidal US pulses with a resonance frequency of 1 MHz, 1000 µs duration, 0.4 duty-cycle, and average acoustic power varying from 2 W to 6 W. Ultrasound waves were generated by a flat circular piezoelectric transducer with a diameter of 25 mm. Cell viability was determined by MTT assay. Structural cellular changes were visualized with a fluorescence microscope. Signs of cytotoxicity such as a decrease in cell viability, chromatin condensation and apoptosis were found. ALA-mediated SDT evokes cytotoxic effects of low intensity US on rat RG2 glioma cells in vitro. This cell line is indicated for further preclinical assessment of SDT in in vivo conditions.

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In order to have consistent and repeatable effects of sonodynamic therapy (SDT) on various cancer cells or tissue lesions we should be able to control a delivered ultrasound energy and thermal effects induced. The objective of this study was to investigate viability of rat C6 glioma cells in vitro depending on the intensity of ultrasound in the region of cells and to determine the exposure time inducing temperature rise above 43 °C, which is known to be toxic for cells. For measurements a planar piezoelectric transducer with a diameter of 20 mm and a resonance frequency of 1.06 MHz was used. The transducer generated tone bursts with 94 µs duration, 0.4 duty-cycle and initial intensity ISATA (spatial averaged, temporal averaged) varied from 0.33 W/cm(2) to 8 W/cm(2) (average acoustic power varied from 1 W to 24 W). The rat C6 glioma cells were cultured on a bottom of wells in 12-well plates, incubated for 24h and then exposed to ultrasound with measured acoustic properties, inducing or causing no thermal effects leading to cell death. Cell viability rate was determined by MTT assay (a standard colorimetric assay for assessing cell viability) as the ratio of the optical densities of the group treated by ultrasound to the control group. Structural cellular changes and apoptosis estimation were observed under a microscope. Quantitative analysis of the obtained results allowed to determine the maximal exposure time that does not lead to the thermal effects above 43 °C in the region of cells for each initial intensity of the tone bursts used as well as the threshold intensity causing cell death after 3 min exposure to ultrasound due to thermal effects. The averaged threshold intensity was found to be about 5.7 W/cm(2).

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The primary goal of this work was to verify experimentally the applicability of the recently introduced time-averaged wave envelope (TAWE) method [J. Wójcik, A. Nowicki, P.A. Lewin, P.E. Bloomfield, T. Kujawska, L. Filipczynski, Wave envelopes method for description of nonlinear acoustic wave propagation, Ultrasonics 44 (2006) 310-329.] as a tool for fast prediction of four dimensional (4D) pulsed nonlinear pressure fields from arbitrarily shaped acoustic sources in attenuating media. The experiments were performed in water at the fundamental frequency of 2.8 MHz for spherically focused (focal length F=80 mm) square (20 x 20 mm) and rectangular (10 x 25mm) sources similar to those used in the design of 1D linear arrays operating with ultrasonic imaging systems. The experimental results obtained with 10-cycle tone bursts at three different excitation levels corresponding to linear, moderately nonlinear and highly nonlinear propagation conditions (0.045, 0.225 and 0.45 MPa on-source pressure amplitude, respectively) were compared with those yielded using the TAWE approach [J. Wójcik, A. Nowicki, P.A. Lewin, P.E. Bloomfield, T. Kujawska, L. Filipczynski, Wave envelopes method for description of nonlinear acoustic wave propagation, Ultrasonics 44 (2006) 310-329.]. The comparison of the experimental results and numerical simulations has shown that the TAWE approach is well suited to predict (to within+/-1 dB) both the spatial-temporal and spatial-spectral pressure variations in the pulsed nonlinear acoustic beams. The obtained results indicated that implementation of the TAWE approach enabled shortening of computation time in comparison with the time needed for prediction of the full 4D pulsed nonlinear acoustic fields using a conventional (Fourier-series) approach [P.T. Christopher, K.J. Parker, New approaches to nonlinear diffractive field propagation, J. Acoust. Soc. Am. 90 (1) (1991) 488-499.]. The reduction in computation time depends on several parameters, including the source geometry, dimensions, fundamental resonance frequency, excitation level as well as the strength of the medium nonlinearity. For the non-axisymmetric focused transducers mentioned above and excited by a tone burst corresponding to moderately nonlinear and highly nonlinear conditions the execution time of computations was 3 and 12h, respectively, when using a 1.5 GHz clock frequency, 32-bit processor PC laptop with 2 GB RAM memory, only. Such prediction of the full 4D pulsed field is not possible when using conventional, Fourier-series scheme as it would require increasing the RAM memory by at least 2 orders of magnitude.

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A novel, free from paraxial approximation and computationally efficient numerical algorithm capable of predicting 4D acoustic fields in lossy and nonlinear media from arbitrary shaped sources (relevant to probes used in medical ultrasonic imaging and therapeutic systems) is described. The new WE (wave envelopes) approach to nonlinear propagation modeling is based on the solution of the second order nonlinear differential wave equation reported in [J. Wójcik, J. Acoust. Soc. Am. 104 (1998) 2654-2663; V.P. Kuznetsov, Akust. Zh. 16 (1970) 548-553]. An incremental stepping scheme allows for forward wave propagation. The operator-splitting method accounts independently for the effects of full diffraction, absorption and nonlinear interactions of harmonics. The WE method represents the propagating pulsed acoustic wave as a superposition of wavelet-like sinusoidal pulses with carrier frequencies being the harmonics of the boundary tone burst disturbance. The model is valid for lossy media, arbitrarily shaped plane and focused sources, accounts for the effects of diffraction and can be applied to continuous as well as to pulsed waves. Depending on the source geometry, level of nonlinearity and frequency bandwidth, in comparison with the conventional approach the Time-Averaged Wave Envelopes (TAWE) method shortens computational time of the full 4D nonlinear field calculation by at least an order of magnitude; thus, predictions of nonlinear beam propagation from complex sources (such as phased arrays) can be available within 30-60 min using only a standard PC. The approximate ratio between the computational time costs obtained by using the TAWE method and the conventional approach in calculations of the nonlinear interactions is proportional to 1/N2, and in memory consumption to 1/N where N is the average bandwidth of the individual wavelets. Numerical computations comparing the spatial field distributions obtained by using both the TAWE method and the conventional approach (based on a Fourier series representation of the propagating wave) are given for circular source geometry, which represents the most challenging case from the computational time point of view. For two cases, short (2 cycle) and long (8 cycle) 2 MHz bursts, the computational times were 10 min and 15 min versus 2 h and 8 h for the TAWE method versus the conventional method, respectively.

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Imaging of living cells or tissues at a microscopic resolution, where GHz frequencies are used, provides a foundation for many new biological applications. The possible temperature increase causing a destructive influence on the living cells should be then avoided. However, there is no information on possible local temperature increases at these very high frequencies where, due to strongly focused ultrasonic beams, nonlinear propagation effects occur. Acoustic parameters of living cells were assumed to be close to those of water; therefore, the power density of heat sources in a water medium was determined as a basic quantity. Hence, the numerical solution of temperature distributions at the frequency of 1 GHz was computed for high and low powers generated by the transducer equal to 0.32 W and 0.002 W. In the first case, typical nonlinear propagation effects were demonstrated and, in the second one, propagation was almost linear. The focal temperature increase obtained in water equaled 14 degrees C for the highest possible theoretical repetition frequency of fr = 10 MHz and for the thermal insulation at the sapphire lens-water boundary. Simultaneously, the scanning velocity of the tested object was assumed to be incomparably low in respect to the acoustic beam velocity. The maximum temperature increase in water occurred exactly at this boundary, being equal there to 20 degrees C. It was shown that, first of all, the very high absorption of water was significant for the temperature distribution in the investigated region, suppressing the focal temperature peaks. Because the temperature increases are proportional to the repetition frequency, so for example, at its practical value of fr = 0.1 MHz, all temperature increases will be 100 times lower than listed above. For the low transducer power of 0.002 W, the corresponding temperature increases were about 140 times lower than those for the high power of 0.32 W. The presented solutions are devoted mainly to the reflection pulse mode; however, they can be also applied for the transmitting (continuous-wave) mode, as shown in an example. Pressure distributions were computed for the acoustic field of the microscope for the first and higher harmonics. Hence, at the frequency of 1 GHz, the effective focal radius in water measured as the -6-dB amplitude pressure drop was found to be 1,1 microm, and 0.7 microm for the second harmonic, independently of the assumed transducer power. So the width of the beam, scanning the living cells in the focal region, was equal to 2.2 microm at the fundamental frequency of 1 GHz.

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Nonlinear propagation effects produced by focused pulses in blood were measured over a 20-cm range, being inspired by diagnostic applications in cardiology. The initial and maximum pressures applied during measurements in blood were equal to 0.40 MPa(pp) and 0.76 MPa(pp), while the pressure estimated at the patient body surface equalled 0.70 MPa(pp). Measurements of the frequency characteristic and the linearity of the ultrasonic probe used in experiments were performed in water. A numerical procedure developed previously was applied in blood to calculate the pressure distribution of its first and second harmonics along the beam axis. The comparison of numerical and measured distributions in blood at a temperature of 37 degrees C showed rather good agreement. Using numerical methods, a proportional growth of the second harmonic with the increased applied initial pressure was first observed, and finally the maximum limiting effect was found. In this way, much higher level of harmonics could be obtained. However, there arise the questions of the transmitting system construction and of the nonuniform resolution in the case of harmonic imaging when increasing the applied initial pressure.

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The authors computed temperature elevations in a three-layer and a four-layer tissue model, assuming the crucial obstetrical case when the ultrasonic pulse propagating through the abdominal wall and the fluid-filled bladder penetrates into soft fetal tissues. To consider nonlinear propagation, the authors applied a new theory of nonlinear increase of absorption recently developed by the first author. Computations were carried out for pulses with a carrier frequency of 3 MHz, duration time of 1.33 micros, and pulse repetition frequency of 3.3 kHz. Similar computations were carried out for a four-layer tissue model corresponding to the third trimester of gestation. The ceramic piezoelectric transducer 2 cm in diameter radiated the ultrasonic beam focused at a distance of 6.5 cm. The intensities at the radiating transducer (at the source) were I(SAPA) = 10 and 5 W/cm2. Temperature elevations and distributions were determined numerically for various values of low-amplitude absorption coefficients assumed to be the same as attenuation coefficients. It was shown in the three-layer tissue model that the maximum temperature elevation can be about 50% higher for nonlinear than for linear propagation. The maximum fetal temperature elevation in this case was 2.36 degrees C for nonlinear and 1.84 degrees C for linear propagation. The temperature elevation in the abdominal wall was lower than those temperatures when the attenuation of the abdominal wall was assumed to be a low value of 0.05 Np/cm.MHz (0.45 dB/cm.MHz). However, when it was increased to 0.16 Np/cm.MHz (1.4 dB/cm.MHz), the temperature elevation of the abdominal wall reached 3.2 degrees C and the maximum fetal elevation was 1.65 degrees C. In such cases, the abdominal wall became the principal source of heat production. In this case, the difference between fetal temperature elevations for nonlinear and linear propagation was only about 10%. The results obtained in the four-layer tissue model, in which the uterus tissue also was represented, show that temperature elevations in this case are about 3.6 times lower than in the three-layer tissue model, with comparable attenuation of the abdominal wall. Differences between nonlinear and linear propagation in the four-layer tissue model are negligible. The temperature elevations obtained were proportional to the pulse repetition frequency, without changing temperature distributions in the ultrasonic beam. In this manner, fetal temperature elevations can be reduced by reducing the repetition frequency.

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The effect of nonlinear propagation in fluid followed by soft tissue was studied both theoretically and experimentally for a most crucial case in obstetrical ultrasonography. For this purpose, short pressure pulses, with the duration time of 1.3 micros and a carrier frequency of 3 MHz, radiated by a concave transducer into water, with maximum intensities up to the value of 18 W/cm2, were computed and measured. The ultrasonic beam had the physical focus at the distance of 6.5 cm, where the highest focal intensity of I(SPPA) = 242 W/cm2 was obtained. In front of the transducer, at a distance of 7 cm, artificial tissue samples prepared on the basis of ground porcine kidney, with a thickness of 0.5, 1.5 and 3 cm, were placed in water. Pressure pulses and their spectral components were produced numerically and measured by means of a PVDF hydrophone in water before and after penetrating the tissue samples. The theoretical analysis and measurements were carried out, in every case, for two signal levels: for a high level assuring nonlinear propagation and for a low one where conditions of linear propagation were fulfilled. In this way, it was possible to compare directly the effects of nonlinear and linear propagation, in every case showing a good conformity of theoretical values with measured ones. A method of determination of the effective frequency response of the hydrophone was elaborated to enable quantitative comparisons of numerical and experimental results. The theoretical part of our study was based on a paper of Wójcik (1998), enabling us to compute the characteristic function of nonlinear increase of absorption. An agreement of up to 10% was obtained when comparing theoretical and measured values of these functions in the investigated beam in water and behind tissue samples. The results obtained showed that the recently given theory of nonlinear absorption, based on the spectral analysis and the elaborated numerical procedures, may be useful in various practical ultrasonic medical problems and also in technological applications.

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An electromagnetic hydrophone has been designed and tested to determine its ability to measure shock wave pulses similar to those produced by lithotripter machines. The principle of operation of the hydrophone, its design and performance are described. The hydrophone was exposed to 4000 shots and peak compressional pressures on the order of 30 MPa without any deleterious effects of its performance and operation. The hydrophone can be calibrated directly by measurement of the magnetic field of the permanent magnet and voltage induced in the electrical conductor. While the spatial resolution of the electromagnetic hydrophone is limited by the length of the vibrating conductor and was determined to be 5 mm, it can be improved. The overall bandwidth of the hydrophone, including its integral preamplifier, had to be limited to 17 MHz; however, the hydrophone appears to reproduce correctly the general shape of the propagating shock wave pulse. The influence of the hydrophone's bandwidth on the measured pulse shape and its amplitude is analysed, and it is shown that it affects rise time and peak compressional pressure. However, no deteriorating influence was observed in reproduction of peak rarefactional pressure.

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The theory of wave reflection from spherical obstacles was applied for determination of the cause of the shadow created by plane wave pulses incident on rigid, steel, gaseous spheres and on spheres made of kidney stones. The spheres were immersed in water which was assumed to be a tissue-like medium. Acoustic pressure distributions behind the spheres with the radii of 1 mm, 2.5 mm and 3.5 mm were determined at the frequency of 5 MHz. The use of the exact wave theory enabled us to take into account the diffraction effects. The computed pressure distributions were verified experimentally at the frequency of 5 MHz for a steel sphere with a 2.5-mm radius. The experimental and theoretical pulses were composed of about three ultrasonic frequency periods. Acoustic pressure distributions in the shadow zone of all spheres were shown in the amplitude axonometric projection, in the grey scale and also as acoustic isobar patterns. Our analysis confirmed existing simpler descriptions of the shadow from the point of view of reflection and refraction effects; however, our approach is more general, also including diffraction effects and assuming the pulse mode. The analysis has shown that gaseous spherical inclusions caused shadows with very high dynamics of acoustic pressures that were about 15 dB higher in relation to all the other spheres. The shadow length, determined as the length at which one observes a 6-dB drop of the acoustic pressure, followed the relation r-6dB = 3.7a2/lambda with the accuracy of about 20% independent of the sphere type. lambda denotes the wavelength and a the sphere radius. Thus, a theoretical possibility of differentiating between gaseous and other inclusions and of estimation of the inclusion size in the millimeter range from the shadow was shown. The influence of the frequency-dependent attenuation on the shadow will be considered in the next study.

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Transient solution of the thermal conductivity equation for the three-dimensional case of the Gaussian ultrasonic focused beam was derived and applied for cases relevant to medical ultrasonography. Quantitative results for the case of a homogeneous medium with constant values of thermal coefficients and constant absorption as well as for the two-layer tissue model used in obstetrics were presented for various diagnostic probes used in ultrasonography. The possible effects of perfusion and nonlinear propagation were neglected. The results obtained are in agreement with results of other authors when considering the steady-state and the infinitely short insonation time. The computations show the influence of the insonation time on the temperature elevation, thus making it possible to introduce its value as a factor in limiting the possible harmful effects in ultrasonography. This has been shown in diagrams presenting the temperature distribution along the beam axis of 6 different diagnostic probes for various insonation times and demonstrating the corresponding temperature decrease when limiting the insonation time to 5 and 1 min. For instance, the highest temperature elevation (for probe number 1, see Table 1) decreases 2.6 and 5 times with respect to the steady-state temperature when the insonation time equals 5 and 1 min, respectively.

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Acoustical pressure distribution behind a steel sphere 5 mm in diameter was measured in water for an incident plane wave with a 2.4-MHz frequency (ka=8pi). Measurements were carried out for continuous and pulse waves at various distance behind the sphere by means of a PVDF membrane hydrophone. The shadow range determined by measurements behind the steel sphere was about 15% shorter than estimated by means of formulae deduced earlier for a rigid sphere. The distributions of the acoustical pressure when measured and computed show almost the same shape. The obtained experimental results to a great extent agree with the theory for the rigid sphere elaborated for ka =4pi to 200 pi. Therefore, these formulae can be used as the first estimation of the shadow range behind an elastic steel sphere. The details of the measurement technique and possible reasons of differences between experiment and theory are discussed.

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