Pavel B. Rosnitskiy

Effect of the angular aperture of medical ultrasound transducers on the parameters of nonlinear ultrasound field with shocks at the focus

Certain modern applications of high-intensity focused ultrasound (HIFU) in medicine use the nonlinear effect of shock front formation in the focal waveform. However, an important problem remains unsolved: determination of transducer parameters that provide the given pressure levels of the shock wave field at the focus required for a specific application. In this paper, simulations based on the Khokhlov-Zabolotskaya equation are performed to test and confirm the hypothesis that angular aperture of the transducer is the main parameter that determines the characteristic amplitude of the shock front and corresponding values for the peak positive and negative pressures at the focus. A criterion for formation of a developed shock in the acoustic waveform, as well as a method for determining its amplitude is proposed. Quantitative dependences of the amplitude of the developed shock and the peak pressures in the wave profile on the angular aperture of the transducer are calculated. The effects of saturation and the range of changes of the shock waveform parameters at the focus are analyzed for a typical HIFU transducer.

Design of HIFU Transducers for Generating Specified Nonlinear Ultrasound Fields

Various clinical applications of high-intensity focused ultrasound have different requirements for the pressure levels and degree of nonlinear waveform distortion at the focus. The goal of this paper is to determine transducer design parameters that produce either a specified shock amplitude in the focal waveform or specified peak pressures while still maintaining quasi-linear conditions at the focus. Multiparametric nonlinear modeling based on the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation with an equivalent source boundary condition was employed. Peak pressures, shock amplitudes at the focus, and corresponding source outputs were determined for different transducer geometries and levels of nonlinear distortion. The results are presented in terms of the parameters of an equivalent single-element spherically shaped transducer. The accuracy of the method and its applicability to cases of strongly focused transducers were validated by comparing the KZK modeling data with measurements and nonlinear full diffraction simulations for a single-element source and arrays with 7 and 256 elements. The results provide look-up data for evaluating nonlinear distortions at the focus of existing therapeutic systems as well as for guiding the design of new transducers that generate specified nonlinear fields.

Setting boundary conditions on the Khokhlov–Zabolotskaya equation for modeling ultrasound fields generated by strongly focused transducers

An equivalent source model is developed for setting boundary conditions on the parabolic diffraction equation in order to simulate ultrasound fields radiated by strongly focused medical transducers. The equivalent source is defined in a plane; corresponding boundary conditions for pressure amplitude, aperture, and focal distance are chosen so that the axial solution to the parabolic model in the focal region of the beam matches the solution to the full diffraction model (Rayleigh integral) for a spherically curved uniformly vibrating source. It is shown that the proposed approach to transferring the boundary condition from a spherical surface to a plane makes it possible to match the solutions over an interval of several diffraction maxima around the focus even for focused sources with F-numbers less than unity. This method can be used to accurately simulate nonlinear effects in the fields of strongly focused therapeutic transducers using the parabolic Khokhlov–Zabolotskaya equation.

Analytical Method for Evaluating the Quality of Acoustic Fields Radiated by a Multielement Therapeutic Array with Electronic Focus Steering

The paper presents an analytical method for calculating and analyzing the quality of 3-D acoustic fields of multielement phased arrays used in noninvasive ultrasound surgical devices. An analytical solution for the far field of each of its elements is used when calculating the array field. This method significantly accelerates calculations while preserving the high accuracy of results as compared to conventional direct numerical integration. Radiation from typical phased arrays is calculated using this approach, and the quality of their dynamic focusing is analyzed. Undesired diffraction effects caused by electronic focus steering are considered: an amplitude decrease in the main maximum and the appearance of grating lobes. The quality of dynamic focusing of the acoustic fields of two practically interesting arrays with a quasi-random element distribution (256 and 1024 elements, respectively), as well as of the regular array consisting of 256 elements is compared. In addition as well, a study is made of how the dimensions of the array elements and their spatial distributions affect the dimensions of the areas in which dynamic focusing is possible without occurrence of strong grating lobes and significant decrease in pressure amplitude at the main focus.

A comparative analysis of the efficiency of probabilistic and possibilistic algorithms for medical diagnostics

Mathematical methods for pattern recognition and algorithms for the classification of diseases based on them are widely used to solve problems of medical diagnostics [1]. In [2], in order to classify functional disorders of the gastrointestinal tract, an algebraic model of the Kora algorithm was applied. In [3–5] it was shown that to solve many problems of medical diagnostics possibilistic methods for making a medical diagnosis are much more efficient. The present work considers a comparative analysis of probabilistic and possibilistic models of diagnostics, as well as Kora algorithms and the results of their application to solving problems of acute appendicitis diagnostics.

Design of HIFU Transducers to Generate Specific Nonlinear Ultrasound Fields

Various clinical applications of high intensity focused ultrasound (HIFU) have different requirements on the pressure level and degree of nonlinear waveform distortion at the focus. Applications that utilize nonlinear waves with developed shocks are of growing interest, for example, for mechanical disintegration as well as for accelerated thermal ablation of tissue. In this work, an inverse problem of determining transducer parameters to enable formation of shocks with desired amplitude at the focus is solved. The solution was obtained by performing multiple direct simulations of the parabolic Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation for various parameters of the source. It is shown that results obtained within the parabolic approximation can be used to describe the focal region of single element spherical sources as well as complex transducer arrays. It is also demonstrated that the focal pressure level at which fully developed shocks are formed mainly depends on the focusing angle of the source and only slightly depends on its aperture and operating frequency. Using the simulation results, a 256-element HIFU array operating at 1.5 MHz frequency was designed for a specific application of boiling-histotripsy that relies on the presence of 90–100 MPa shocks at the focus. The size of the array elements and focusing angle of the array were chosen to satisfy technical limitations on the intensity at the array elements and desired shock amplitudes in the focal waveform. Focus steering capabilities of the array were analysed using an open-source T-Array software developed at Moscow State University.

Dependence of inertial cavitation induced by high intensity focused ultrasound on transducer F-number and nonlinear waveform distortion

Pulsed high intensity focused ultrasound was shown to enhance chemotherapeutic drug uptake in tumor tissue through inertial cavitation, which is commonly assumed to require peak rarefactional pressures to exceed a certain threshold. However, recent studies have indicated that inertial cavitation activity also correlates with the presence of shocks at the focus. The shock front amplitude and corresponding peak negative pressure (p -) in the focal waveform are primarily determined by the transducer F-number: less focused transducers produce shocks at lower p -. Here, the dependence of inertial cavitation activity on the transducer F-number was investigated in agarose gel by monitoring broadband noise emissions with a coaxial passive cavitation detector (PCD) during pulsed exposures (pulse duration 1 ms, pulse repetition frequency 1 Hz) with p- varying within 1-15 MPa. Three 1.5 MHz transducers with the same aperture, but different focal distances (F-numbers 0.77, 1.02, 1.52) were used. PCD signals were processed to extract cavitation probability, persistence, and mean noise level. At the same p -, all metrics indicated enhanced cavitation activity at higher F-numbers; specifically, cavitation probability reached 100% when shocks formed at the focus. These results provide further evidence supporting the excitation of inertial cavitation at reduced p - by waveforms with nonlinear distortion and shocks.

Development of a freely available simulator with graphical interface for modeling nonlinear focused ultrasound fields with shocks

Measurement-based modeling is gaining acceptance as a standard tool for characterizing the nonlinear fields of existing therapeutic ultrasound devices and designing new ones. Here, a freely available simulation tool is presented for modeling axially symmetric, strongly nonlinear HIFU beams with shocks in a layered propagation medium such as water and different types of tissue. Two nonlinear wave equations are included in the simulator: the KZK equation generalized to include an equivalent source boundary condition for strongly focused beams and the Westervelt equation in a nonlinear wide-angle parabolic representation. Both equations are solved in the frequency domain and permit definition of the HIFU transducer as an annular array. The geometrical parameters and power output of the array, electronic focus steering along the beam axis, and acoustic properties of the layered propagation medium can be configured via graphical interface. Visualization and output of various acoustic field parameters such as peak positive and negative pressures, shock amplitude, intensity, heat deposition rate, and total power of a beam are also provided. The simulator can be used for transducers without ideal symmetry through definition of an equivalent radially symmetric source. Widespread availability of such simulation tools will help advance standardized utilization of measurement-based modeling and facilitate the adoption of such approaches for HIFU treatment planning. [Work supported by NIH R01EB7643, R01EB025187, and RSF №14-12-00974.]Measurement-based modeling is gaining acceptance as a standard tool for characterizing the nonlinear fields of existing therapeutic ultrasound devices and designing new ones. Here, a freely available simulation tool is presented for modeling axially symmetric, strongly nonlinear HIFU beams with shocks in a layered propagation medium such as water and different types of tissue. Two nonlinear wave equations are included in the simulator: the KZK equation generalized to include an equivalent source boundary condition for strongly focused beams and the Westervelt equation in a nonlinear wide-angle parabolic representation. Both equations are solved in the frequency domain and permit definition of the HIFU transducer as an annular array. The geometrical parameters and power output of the array, electronic focus steering along the beam axis, and acoustic properties of the layered propagation medium can be configured via graphical interface. Visualization and output of various acoustic field parameters such as p...

Various approaches for designing phased arrays for high-intensity focused ultrasound therapies: From sparse to fully-populated configurations

High-intensity focused ultrasound (HIFU) therapies are often performed using multi-element phased arrays. Independent variation of the amplitudes and phases at the array elements allows electronic steering of the focus and compensation for aberrations. To suppress the formation of grating lobes, the arrangement of the array elements should be non-periodic. Three approaches that have been recently employed in our studies to solve this problem are presented and discussed: a random element arrangement [L.R. Gavrilov and J.W. Hand, IEEE Trans. UFFC 2000], a multi-armed spiral arrangement [V.A. Khokhlova et al., Physics Procedia 2016], and recently proposed array design with tight packing of the elements based on the capacity-constrained tessellation [P.B. Rosnitskiy et al., IEEE UFFC 2018]. The efficiency of two arrays with the same geometric and physical parameters is compared: a 256-element array with a compact 16-spirals layout of circular elements and a fully populated array comprising polygonal elements of equal area. It is shown that for the same intensity at the elements, the fully-populated array provides twofold higher total power while maintaining the same electronic focusing capabilities as compared to the spiral one which can be beneficial for high-power applications such as histotripsy. [The work was supported by NIH R01EB7643 and R01EB025187, RFBR 17-02-00261, and Ph.D. student stipends from the “Basis” Foundation and of the President of Russia SP-2644.2018.4.]High-intensity focused ultrasound (HIFU) therapies are often performed using multi-element phased arrays. Independent variation of the amplitudes and phases at the array elements allows electronic steering of the focus and compensation for aberrations. To suppress the formation of grating lobes, the arrangement of the array elements should be non-periodic. Three approaches that have been recently employed in our studies to solve this problem are presented and discussed: a random element arrangement [L.R. Gavrilov and J.W. Hand, IEEE Trans. UFFC 2000], a multi-armed spiral arrangement [V.A. Khokhlova et al., Physics Procedia 2016], and recently proposed array design with tight packing of the elements based on the capacity-constrained tessellation [P.B. Rosnitskiy et al., IEEE UFFC 2018]. The efficiency of two arrays with the same geometric and physical parameters is compared: a 256-element array with a compact 16-spirals layout of circular elements and a fully populated array comprising polygonal elements ...

Design and characterization of a 2-dimensional focused 1.5-MHz ultrasound array with a compact spiral arrangement of 256 circular elements

Multi-element ultrasound arrays are increasingly used in clinical practice for both imaging and therapy. In therapy, they allow electronic steering, aberration correction, and focusing. To avoid grating lobes, an important requirement for such an array is the absence of periodicity in the arrangement of the elements. A convenient solution is the arrangement of the elements along spirals. The objective of this work was to design, fabricate, and characterize an array for boiling histotripsy applications that is capable of generating shock waves in the focus of up to 100 MPa peak pressure while having a reasonable electronic steering range [Khokhlova et al., Physics Procedia 87 (2016)].