A hybrid boundary element model is proposed for the simulation of large piezoelectric micromachined ultrasonic transducer (PMUT) arrays in immersion. Multiphysics finite element method (FEM) simulation of a single-membrane structure is used to determine stiffness and piezoelectrically induced actuation loading of the membranes. To simulate the arrays of membranes in immersion, a boundary element method is employed, wherein membrane structures are modeled by a surface mesh that is coupled mechanically by mass, stiffness, and damping matrices, and acoustically by a mutual impedance matrix. A multilevel fast multipole algorithm speeds up computation time and reduces memory usage, enabling the simulation of thousands of membranes in a reasonable time. The model is validated with FEM for a small 3 3 matrix array for both square and circular membrane geometries. Two practical optimization examples of large PMUT arrays are demonstrated: membrane spacing of a 7 7 matrix array with circular membranes, and material choice and top electrode coverage of a 32-element linear array with 640 circular membranes. In addition, a simple analytical approach to electrode optimization based on normal mode theory is verified.
A boundary element model provides great flexibility for the simulation of membrane-type micromachined ultrasonic transducers (MUTs) in terms of membrane shape, actuating mechanism, and array layout. Acoustic crosstalk is accounted for through a mutual impedance matrix which captures the primary crosstalk mechanism of dispersive-guided modes generated at the fluid-solid interface. However, finding the solution to the fully-populated boundary element matrix equation using standard techniques requires computation time and memory usage which scales by the cube and by the square of the number of nodes, respectively, limiting simulation to a small number of membranes. We implement a solver with improved speed and efficiency through the application of a multi-level fast multipole algorithm (FMA). By approximating the fields of collections of nodes using multipole expansions of the free-space Green’s function, an FMA solver can enable the simulation of hundreds of thousands of nodes while incurring an approximation error that is controllable. Convergence is drastically improved using a problem-specific block-diagonal preconditioner. We demonstrate the solver’s capabilities by simulating a 32-element 7 MHz 1-D CMUT phased array with 2880 membranes. The array is simulated using 233,280 nodes for a very wide frequency band up to 50 MHz. For a simulation with 15,210 nodes, the FMA solver performed 10-times faster and used 32-times less memory than a standard solver based on LU decomposition We investigate the effects of mesh density and phasing on the predicted array response and find that it is necessary to use about 7 nodes over the width of the membrane to observe convergence of the solution–even below the first membrane resonance frequency–due to the influence of higher-order membrane modes.
The drive toward minimally invasive surgery has yielded multiple benefits for patients but has also increased the incidence of pseudoaneurysms (PSA). The current standard of care is ultrasound‐guided thrombin injection to coagulate blood in the PSA sac and seal the ruptured vessel. There is, however, a risk of downstream thrombosis if thrombin escapes into the communicating vessel and this limits patient eligibility for thrombin injection. In this study, the feasibility of using magnetic targeting to reduce the risk of distal thrombosis is investigated. Thrombin‐loaded magnetic microbubbles are formulated and injected into tissue‐mimicking phantoms of PSAs with different geometries using either saline or whole (equine) blood. Ultrasound imaging is used to quantify the concentration of bubbles remaining in the sac with and without application of a custom‐built magnetic array. An absorbance‐based assay is also used to quantify the concentration of thrombin escaping from the sac. Magnetic targeting enables a significant increase in thrombin retention in all femoral artery PSA models except one, with up to 97% ± 2.5% of the injected thrombin being retained. It is also confirmed that the enzymatic activity of thrombin is maintained, and that clot formation can be successfully achieved in whole blood.
Advances in magnetic materials have enabled the development of new therapeutic agents which can be localised by external magnetic fields. These agents offer a potential means of improving treatment targeting and reducing the toxicityrelated side effects associated with systemic delivery. Achieving sufficiently high magnetic fields at clinically relevant depths in vivo, however, remains a challenge. Similarly, there is a need for techniques for real-time monitoring that do not rely on magnetic resonance imaging (MRI). Here, we present a hand-held device to meet these requirements, combining an array of permanent magnets and a thin 64-element capacitive micromachined ultrasound transducer (CMUT) interfaced to a real-time imaging system.Drug carrier localisation was assessed by measuring the terminal velocity of magnetic microbubbles in a column of fluid above the magnetic array. It was found that the magnetic pull force was sufficient to overcome buoyancy at equivalent tissue depths of at least 35 mm and that the median terminal velocity ranged from 0.7 -20 µm/s over the distances measured. A Monte Carlo study was performed to estimate capture effectiveness in tumour microvessels over a range of different tissue depths and flow rates. Finally, B-mode and contrast-enhanced ultrasound imaging were demonstrated using a gel flow phantom containing a 1.6 mm diameter vessel. Real-time monitoring provided visual confirmation of retention of magnetic microbubbles along the vessel wall at a flow rate of 0.5 mL/min. These results indicate that the system can successfully retain and image magnetic microbubbles at tissue depths and flow rates relevant for clinical applications such as molecular ultrasound imaging of artherosclerosis, sonodynamic and antimetabolite cancer therapy, and clot dissolution via sonothrombolysis.
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