Efficient 3-D Finite Element Modeling of Periodic XBAR Resonators.

An efficient technique is presented for 3-D finite element modeling of large-scale periodic excited bulk acoustic resonator (XBAR) resonators in the time-harmonic domain. In this technique, a domain decomposition scheme is used to decompose the computational domain into many small subdomains whose FE subsystems can be factorized with a direct sparse solver at a low cost. Transmission conditions (TCs) are enforced to interconnect adjacent subdomains, and a global interface system is formulated and solved iteratively. To accelerate the convergence, a second-order TC (SOTC) is designed to make the subdomain interfaces transparent for propagating and evanescent waves. An effective forward-backward preconditioner is constructed that when combined with the SOTC significantly reduce the number of iterations at no additional cost. Numerical results are given to demonstrate the accuracy, efficiency, and capability of the proposed algorithm.

Hierarchical Cascading Algorithm for 2-D FEM Simulation of Finite SAW Devices.

Application of the finite-element method (FEM) for the simulation of surface acoustic wave (SAW) devices has been constrained by the large number of degrees of freedom required, resulting in large memory usage and long computation times. We propose a new 2-D algorithm that takes advantage of the periodic structure typical of SAW devices. The device is partitioned into small, repeatedly occurring building blocks. Only unique building blocks are simulated with FEM. The device geometry is presented as a hierarchical tree of cascading operations, where smaller blocks are combined into larger blocks. This is equivalent to the full FEM simulation of the device, implying the drastic reduction of memory consumption and simulation time for structures with a high degree of periodicity. The method is verified against FEM/BEM-based software. To ensure accurate and efficient simulation, the boundary conditions should be chosen according to the anisotropy of the substrate crystal.

High intensity focused ultrasound induced in vivo large volume hyperthermia under 3D MRI temperature control.

PURPOSE: Mild hyperthermia can be used as an adjuvant therapy to enhance radiation therapy or chemotherapy of cancer. However, administering mild hyperthermia is technically challenging due to the high accuracy required of the temperature control. MR guided high-intensity focused ultrasound (MR-HIFU) is a technology that can address this challenge. In this work, accurate and spatially uniform mild hyperthermia is demonstrated for deep-seated clinically relevant heating volumes using a HIFU system under MR guidance. METHODS: Mild hyperthermia heating was evaluated for temperature accuracy and spatial uniformity in 11 in vivo porcine leg experiments. Hyperthermia was induced with a commercial Philips Sonalleve MR-HIFU system embedded in a 1.5T Ingenia MR scanner. The operating software was modified to allow extended duration mild hyperthermia. Heating time varied from 10 min up to 60 min and the assigned target temperature was 42.5 °C. Electronic focal point steering, mechanical transducer movement, and dynamic transducer element switch-off were exploited to enlarge the heated volume and obtain uniform heating throughout the acoustic beam path. Multiple temperature mapping images were used to control and monitor the heating. The magnetic field drift and transducer susceptibility artifacts were compensated to enable accurate volumetric MR thermometry. RESULTS: The obtained mean temperature for the target area (the cross sectional area of the heated volume at focal depth primarily used to control the heating) was on average 42.0 ± 0.6 °C. Temperature uniformity in the target area was evaluated using T10 and T90, which were 43.1 ± 0.6 and 40.9 ± 0.6 °C, respectively. For the near field, the corresponding temperatures were 39.3 ± 0.8 °C (average), 40.6 ± 1.0 °C (T10), and 38.0 ± 0.9 °C (T90). The sonications resulted in a concise heating volume, typically in the shape of a truncated cone. The average depth reached from the skin was 86.9 mm. The results show that the heating algorithm was able to induce deep heating while keeping the near-field temperature uniform and at a safe level. CONCLUSIONS: The capability of MR-HIFU to induce accurate, spatially uniform, and robust mild hyperthermia in large deep-seated volumes was successfully demonstrated through a series of in vivo animal experiments.

Stochastic ray tracing for simulation of high intensity focal ultrasound therapy.

An algorithm is presented for rapid simulation of high-intensity focused ultrasound (HIFU) fields. Essentially, the method combines ray tracing with Monte Carlo integration to evaluate the Rayleigh-Sommerfeld integral. A large number of computational particles, phonons, are distributed among the elements of a phase-array transducer. The phonons are emitted into random directions and are propagated along trajectories computed with the ray tracing method. As the simulation progresses, an improving stochastic estimate of the acoustic field is obtained. The method can adapt to complicated geometries, and it is well suited to parallelization. The method is verified against reference simulations and pressure measurements from an ex vivo porcine thoracic tissue sample. Results are presented for acceleration with graphics processing units (GPUs). The method is expected to serve in applications, where flexibility and rapid computation time are crucial, in particular clinical HIFU treatment planning.

High intensity focused ultrasound with large aperture transducers: a MRI based focal point correction for tissue heterogeneity.

PURPOSE: The risk of undesired tissue damage to thoracic cage, heart, and lung during MR guided HIFU ablations of breast cancer can be greatly reduced if a phased array transducer design with a lateral beam direction is used in combination with a large aperture. The disadvantage is an increased sensitivity to focus aberrations due to tissue heterogeneity. Here, the authors propose to restore the focal coherence by using a matched aperture phase correction, which is based on a noninvasively obtained tissue model. METHODS: The method combines high resolution MRI with ultrasound wave measurements of different tissue types to determine a phase correction, which compensates focal point aberrations caused by tissue heterogeneity. 3D segmentation of tissue is used to quantify the relative proportion of each tissue type along a line running from the center of each element of the phased array to the target focal point. RESULTS: For tissue types with a celerity difference of 3%, the proposed method allows to quantify the phase aberration with an accuracy of 6° ± 20° and a correlation factor R(2) = 0.95. Using the refocusing method for a complex heterogeneous phantom resulted in 95% of the maximal pressure, whereas only 70% of the maximal pressure is obtained in absence of any phase correction. CONCLUSIONS: Since the proposed refocusing algorithm is compatible with a standard interventional preplanning and requires only a minimal amount of processing, it presents a promising approach to compensate for aberration in heterogeneous tissues such as the human breast.

Second-harmonic reflectors on 128 degrees LiNbO3.

In this work, we study theoretically the operation of long surface acoustic wave reflectors, comprising a large number of electrodes, at the fundamental and second harmonic frequencies on the 128 degrees LiNbO3 substrate for various electrode thicknesses and metallization ratios. Numerical simulations utilizing tailored test structures and time gating indicate that the reflectivity of the second-harmonic reflectors can be very high for certain geometries. Furthermore, our simulations suggest that inside the stopband the total losses for the second harmonic are of the same order as those for operation at the fundamental harmonic.

Harmonic admittance and dispersion equations--the theorem.

The harmonic admittance is known as a powerful tool for analyzing the excitation and propagation of surface acoustic waves (SAWs) in periodic electrode arrays. In particular, the dispersion relationships for open- and short-circuited systems are indicated, respectively, by the zeros and poles of the harmonic admittance. Here, we show that a strict reverse relationship also exists: the harmonic admittance of a periodic system of electrodes may always be expressed as the ratio of two determinants, which have been specifically constructed to describe the eigen-modes of the open- and short-circuited systems. There is no need to solve these equations to find the admittance. The existence of a connection between the excitation and propagation problems was recognized within the coupling-of-modes theory by Chen and Haus and was recently used to model surface transverse waves by Koskela et al., but a rigorous mathematical proof was only found later by Biryukov. Here, we reproduce this theorem in detail, give some examples of calculations based on this theorem, and compare the results with measured admittance curves.