Evaluation of a novel therapeutic focused ultrasound transducer based on Fermat’s spiral

Abstract

The purpose of this study was to evaluate a novel phased array transducer design rule for therapeutic focused ultrasound applications. This design rule uses the discretized Fermat’s spiral to determine the positioning of the transducer elements for a given number of elements and f-number. Using this principle, three variations of Fermat’s spiral were generated, aimed at (1) grating lobe minimization, (2) side lobe minimization, and (3) an optimized element packing efficiency. For each spiral, sparse layouts using identical circular elements and fully populated layouts based on additional Voronoi tessellation were evaluated numerically. Evaluation criteria included the element size distribution, beam steering capabilities, focal plane pressure distribution, prefocal pressure distribution, and practical considerations. Finally, one Voronoi-tessellated design with a focal length and aperture diameter of 16 cm and a natural frequency of 1.3 MHz was evaluated experimentally through hydrophone measurements. The numerical evaluation showed that while sparse arrays possess superior beam steering capabilities for a given number of elements, the focal point quality and prefocal pressure distribution is substantially more favorable when using the Voronoi-tessellated designs. Beam steering was shown to be feasible with the tessellated designs for lateral deflections up to 10 mm and axial deflections up to 20 mm. The experimental evaluation showed that such a transducer is capable of inducing 40.00 MPa rarefactional and 237.50 MPa compressional peak pressure levels at 800 W instantaneous acoustic output power under free-field conditions, making the system potentially relevant for thermal ablation therapy, histotripsy applications, and shockwave-enhanced heating.