Analytical expressions for the time-domain Green's function that exactly solve the wave equation for power-law media with an attenuation term that is proportional to frequency to the power were recently derived. These analytical expressions are causal for power-law exponents less than one and noncausal for power-law exponents greater than or equal to one. A causal expression for the lossy impulse response for a circular piston is obtained for power-law exponent when the impulse response of the time-domain Rayleigh-Sommerfeld integral is evaluated by superposing the causal Green's function in space and in time. The lossy impulse response is also computed in the frequency-domain for the same piston. Numerical results are computed in the time and frequency-domains for a circular piston with a radius of 15mm. Problems with aliasing are identified in the frequency-domain impulse response calculation, whereas these problems are avoided in the time-domain calculation.
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.
High-intensity focused ultrasound is used in many therapeutic applications such as drug activation/drug delivery, hyperthermia, cancer therapy, ultrasound surgery and myocardial ablation. Various ultrasonic systems have been proposed for these therapeutic applications. While many applicators produce adequate power levels, multiple element ultrasound phased arrays adjust for phase aberrations, focus around obstructions such as bone and/or air spaces (lungs), and follow, in real time, a moving target. Since large aperture arrays with several hundred elements are required, design compromises keep the element count and fabrication cost at a reasonable level. These trade-offs, which optimize the array aperture with respect to element count, often result in a non-ideal aspect ratio (element width to thickness), leading to lateral mode vibrations which reduce the electrical to acoustical efficiency to about 10 - 20%. These vibrations are easily observed with a laser interferometer system. Piezo composite technology, which eliminates the non-ideal aspect ratio by dividing the individual array elements into long, thin rods, provides a solution to this problem. The spaces between the rods are filled with a polymer to provide structural support and allow deposition of electrode layers to interconnect individual rods and to outline array elements. Several piezo composite transducers have been tested, and initial results show a greatly improved beam pattern and increased efficiency. Power handling capability of composites has recently improved allowing outputs in excess of 10 watts/cm2 with efficiencies greater than 60%. This is sufficient for many therapeutic applications.
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