Staff

Abstract:
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.

Keywords:
Nonliear propagation, Envelope waves, Fast calculations

Abstract:
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. Wojcik, 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 approximateratio 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/N)**2, 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.

Keywords:
Nonliear propagation, Envelope waves, Fast calculations

Abstract:
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°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°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 μm, and 0.7 μm 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 μm at the fundamental frequency of 1 GHz.

Keywords:
Temperature, Acoustic microscopy, Living cells, Temperature increase, Pressure

Abstract:
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 MPapp and 0.76 MPapp, while the pressure estimated at the patient body surface equalled 0.70 MPapp. 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°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.

Keywords:
Ultrasound, Pulses, Nonlinear propagation, Blood, Cardiology

Abstract:
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 μs 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 ISPPA= 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.

Keywords:
Ultrasound, Pulses, Nonlinear propagation, Diagnostics

Abstract:
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 tissuelike 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 = 3.7a2λ with the accuracy of about 20% independent of the sphere type. λ 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.

Keywords:
Shadow, Pulses, Spheres, Ultrasonography

Abstract:
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.

Keywords:
Temperature, Ultrasonography, Time, Hazard

Abstract:
Transient solutions of the thermal conductivity equation for the two-dimensional case of an elongated cylíndrical focus in the ultrasonic beam were derived and applied for lithotripsy and obstetrical ultrasonography. Assuming uniform and Gaussian distributions in the focus of the beam cross section, it was possible to estimate the temperature elevation arising in lithotripsy for various repetition frequencies of shock-wave pulses and for various radii of the beam. In obstetrical ultrasonography where the blood perfusion is difficult to determine, the authors suggested that the insonation time be used as the decisive factor for the temperature determination. Values of focal intensities were found necessary to increase the tissue temperature by 1°C as a function of the insonation time and the beam radius which exclude the possibility of any hazardous effect caused by temperature elevation.

Keywords:
Lithotripsy, Obstetrics, Ultrasonography, Temperature, Hazard