T. Kujawska

Nonlinear and linear propagation of diagnostic ultrasound pulses

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.

Fast prediction of pulsed nonlinear acoustic fields from clinically relevant sources using Time-Averaged Wave Envelope approach: comparison of numerical simulations and experimental results

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. Filipczyński, 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. Filipczyński, 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.

Determination of nonlinear medium parameter B/A using model assisted variable-length measurement approach.

This work addresses the difficulties in the measurements of the nonlinear medium parameter B/A and presents a modification of the finite amplitude method (FAM), one of the accepted procedures to determine this parameter. The modification is based on iterative, hybrid approach and entails the use of the versatile and comprehensive model to predict distortion of the pressure-time waveform and its subsequent comparison with the one experimentally determined. The measured p-t waveform contained at least 18 harmonics generated by 2.25 MHz, 29 mm effective diameter, single element, focused PZT source (f-number 3.5) and was recorded by Sonora membrane hydrophone calibrated in the frequency range 1-40 MHz. The hydrophone was positioned coaxially at the distal end of the specially designed, two-section assembly comprising of one, fixed length (60mm), water-filled cylindrical container and the second, variable length (60-120 mm) container that was filled with unknown medium. The details of the measurement chamber are described and the reasons for this specific design are analyzed. The data were collected with the variable length chamber filled with 1.3-butanediol, which was used as a close approximation of tissue mimicking phantom. The results obtained provide evidence that a novel combination of the FAM with the semi-empirical nonlinear propagation model based on the hyperbolic operator is capable of reducing the overall uncertainty of the B/A measurements as compared to those reported in the literature. The overall uncertainty of the method reported here was determined to be ±2%, which enhances the confidence in the numerical values of B/A measured for different, clinically relevant media. Optimization of the approach is also discussed and it is shown that it involves an iterative procedure that entails a careful selection of the acoustic source and its geometry and the axial distance over which the measurements need to be performed. The optimization also depends critically on the experimental determination of the source surface pressure amplitude.

Temperature elevations computed for three-layer and four-layer obstetrical tissue models in nonlinear and linear ultrasonic propagation cases

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.

Electromagnetic hydrophone for pressure determination of shock wave pulses

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 hydrophones 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.

Impact of thermal effects induced by ultrasound on viability of rat C6 glioma cells

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).

Temperature elevation in focused Gaussian ultrasonic beams at various insonation times

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.

Determination of Tissue Thermal Conductivity by Measuring and Modeling Temperature Rise Induced in Tissue by Pulsed Focused Ultrasound

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).

NONLINEAR NATIVE PROPAGATION EFFECTS OF DIAGNOSTIC ULTRASOUND COMPUTED AND MEASURED IN BLOOD

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.

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

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.