Xiaozheng Zeng

Evaluation of the angular spectrum approach for simulations of near-field pressures

The implementation of the angular spectrum approach based on the two-dimensional fast Fourier transform is evaluated for near-field pressure simulations of square ultrasound transducers, where the three-dimensional pressure field is calculated from the normal velocity distribution on the transducer surface. The pressure field is propagated in the spatial frequency domain with the spatial propagator or the spectral propagator. The spatial propagator yields accurate results in the central portion of the computational grid while significant errors are produced near the edge due to the finite extent of the window applied to the spatial propagator. Likewise, the spectral propagator is inherently undersampled in the spatial frequency domain, and this causes high frequency errors in the computed pressure field. This aliasing problem is alleviated with angular restriction. The results show that, in nonattenuating media, the spatial propagator achieves smaller errors than the spectral propagator after the region of interest is truncated to exclude the windowing error. For pressure calculations in attenuating media or with apodized pistons as sources, the spatial and spectral propagator achieve similar accuracies. In all simulations, the angular spectrum calculations with the spatial propagator take more time than calculations with the spectral propagator.

Optimal simulations of ultrasonic fields produced by large thermal therapy arrays using the angular spectrum approach

The angular spectrum approach is evaluated for the simulation of focused ultrasound fields produced by large thermal therapy arrays. For an input pressure or normal particle velocity distribution in a plane, the angular spectrum approach rapidly computes the output pressure field in a three dimensional volume. To determine the optimal combination of simulation parameters for angular spectrum calculations, the effect of the size, location, and the numerical accuracy of the input plane on the computed output pressure is evaluated. Simulation results demonstrate that angular spectrum calculations performed with an input pressure plane are more accurate than calculations with an input velocity plane. Results also indicate that when the input pressure plane is slightly larger than the array aperture and is located approximately one wavelength from the array, angular spectrum simulations have very small numerical errors for two dimensional planar arrays. Furthermore, the root mean squared error from angular spectrum simulations asymptotically approaches a nonzero lower limit as the error in the input plane decreases. Overall, the angular spectrum approach is an accurate and robust method for thermal therapy simulations of large ultrasound phased arrays when the input pressure plane is computed with the fast nearfield method and an optimal combination of input parameters.

A Waveform Diversity Method for Optimizing 3-D Power Depositions Generated by Ultrasound Phased Arrays

A waveform-diversity-based approach for 3-D tumor heating is compared to spot scanning for hyperthermia applications. The waveform diversity method determines the excitation signals applied to the phased array elements and produces a beam pattern that closely matches the desired power distribution. The optimization algorithm solves the covariance matrix of the excitation signals through semidefinite programming subject to a series of quadratic cost functions and constraints on the control points. A numerical example simulates a 1444-element spherical-section phased array that delivers heat to a 3-cm-diameter spherical tumor located 12 cm from the array aperture, and the results show that waveform diversity combined with mode scanning increases the heated volume within the tumor while simultaneously decreasing normal tissue heating. Whereas standard single focus and multiple focus methods are often associated with unwanted intervening tissue heating, the waveform diversity method combined with mode scanning shifts energy away from intervening tissues where hotspots otherwise accumulate to improve temperature localization in deep-seated tumors.

Fast-pressure field calculations applied to large spherical ultrasound phased arrays designed for thermal therapy

Large spherical ultrasound phased arrays are ideal for simulation studies of thermal therapy devices designed for noninvasive breast cancer treatments. In a spherical array, circular sources packed in a dense hexagonal arrangement facilitate the most efficient use of the available aperture. Circular sources are also preferred for simulations of large phased arrays because pressure fields are computed more rapidly for circular pistons than for any other transducer geometry. The computation time is further reduced for circular transducers with grid sectoring. With this approach, the grid of computed pressures is divided into several regions, and then grid sectoring applies more abscissas in regions where the pressure integral converges slowly and fewer abscissas where the integral converges rapidly. As a result, the peak value of the numerical error is roughly the same in each sector, so the maximum numerical error in the computed field is maintained while the computation time is significantly reduced. The grid sectoring approach is extended to three dimensions (3D) for pressure field calculations with spherical arrays. In 3D calculations, the sectors are represented by cones, and the intersections between the computational grid and these cones define the boundaries required for grid sectoring. When these cone structures are applied to spherical phased arrays, 3D grid sectoring calculations rapidly compute the pressure fields so that the time required for array design and evaluation is substantially reduced.

Computer modeling of hyperthermia temperature distributions produced by hybrid RF/US phased arrays

Simulation studies of hyperthermia as an adjuvant treatment for locally advanced breast cancer (LABC) show that temperature distributions are significantly improved with hybrid devices that combine ultrasound (US) and radio‐frequency (RF) electromagnetic phased arrays. Ultrasound phased arrays, which generate relatively small focal spots in deep targets, are limited by intervening tissue heating in 60‐minute hyperthermia treatments of large LABC tumors. In contrast RF phased arrays are regional heating devices with limited penetration depths. This combination offsets the drawbacks of each modality while offering multiple opportunities for optimization in LABC tumors. One optimization strategy partitions the tumor into two regions that are targeted individually by each modality. This approach targets the portion of the tumor proximal to the RF applicator and/or the skin surface with the RF component, and the US component delivers heat to the tumor in regions that the RF fails to reach. This heating strateg...

Rapid Simulations of Large Ultrasound Therapy Arrays with the Fast Nearfield Method and the Angular Spectrum Approach

Simulations of time‐harmonic pressure fields generated by large ultrasound therapy arrays are extremely time‐consuming because of the large number of transducer elements and the size of the computational volume. After pressures are calculated for thermal therapy simulations on a computational grid that extends one hundred wavelengths or more in all three directions, subsequent heat transfer calculations require half‐wavelength or better sampling, resulting in a very large number of pressure calculations that require a considerable amount of computation time. The time required is dramatically reduced with simulation methods that determine the source plane distribution with the fast nearfield method (FNM) and then propagate the pressure in parallel planes with the angular spectrum approach (ASA). The combination of the FNM and ASA for fast pressure calculations is numerically accurate and time‐efficient, achieving smaller errors than ASA calculations that are based on the input particle velocity distributio...

Multiplanar angular spectrum approach for fast simulations of ultrasound therapy arrays

Pressure field modeling with ultrasound phased arrays designed for thermal therapy is extremely time‐consuming due to the large computational grids required and because each array contains a large number of elements. The angular spectrum approach (ASA) computes wave propagation in parallel planes with a two‐dimensional fast Fourier transform in considerably less time than point‐by‐point direct integral methods. The conventional ASA, which performs well with planar and small focused radiators, encounters numerical problems in simulations of large phased arrays. These errors are caused in part by the narrowing of the beam in the focal region, which produces a significant increase in the spatial frequency content. The numerical errors are reduced with the inclusion of additional source planes within the computational domain. These are distributed such that the distance between adjacent source planes is small near the focal zone, and the spacing between source planes grows progressively larger as the distance...

Optimal control point distributions for waveform diversity.

Waveform diversity is a method for tumor heating with ultrasound phased arrays that extend the concept of multiple focusing to achieve an optimal sequence of power depositions. Waveform diversity minimizes the power deposited at control points in normal tissue while maximizing the power at control points in the tumor through an approach that employs semi‐definite programming. As with other spot scanning and multiple focusing techniques, the performance of waveform diversity depends on the location of the control points. For example, single spot scanning is limited by intervening tissue heating, so the ideal spot scanning approach in large tumors focuses on the back half of the tumor and allows intervening tissue heating to fill in the remaining tumor region. In contrast, waveform diversity combined with mode scanning tends to preferentially deliver heat beyond control points placed in the tumor. In an effort to exploit this feature, the energy delivered to control points on the front face of the tumor is ...

P1B-1 Optimization of Power Distributions Produced by Ultrasound Phased Arrays through Waveform Diversity

The objective of hyperthermia cancer therapy is to elevate the tumor temperature to approximately 43degC while maintaining normal temperature in healthy tissue. This goal can be achieved through a waveform diversity method that optimizes the covariance matrix of the excitation signals applied to array elements. This paper presents the computer simulation of a cylindrical section ultrasound phased array using the waveform diversity method to heat a spherical tumor embedded in a 3D biological tissue model. With this hearing strategy, optimal excitation sequences are obtained and desirable power depositions and temperature distributions are achieved.

Sector-vortex scanning for hyperthermia with a large square ultrasound phased array aperture

Planar ultrasound (US) phased arrays with square element are easier to fabricate and model than other concave shaped phased arrays. Combined with phases derived for single spot focusing, the sector-vortex phase scheme can be applied to the square planar array to generate a vortex shaped pressure field that can be controlled by the mode number M. Increasing the mode number M also increases the diameter of the annular focus. The location of the annular focus can be moved along the axis or off axis by steering the single spot focus. The weight of the phase for single spot focusing can control the axial length of the sector-vortex pattern. Superposing the SAR of multiple modes can heat large tumors with diameters up to 5 cm by broadening the temperature distribution