Improved intercostal HIFU ablation using a phased array transducer based on Fermat’s spiral and Voronoi tessellation: A numerical evaluation

Purpose: A major complication for abdominal High Intensity Focused Ultrasound (HIFU) applications is the obstruction of the acoustic beam path by the thoracic cage, which absorbs and reflects the ultrasonic energy leading to undesired overheating of healthy tissues in the pre-focal area. Prior work has investigated the determination of optimized transducer apodization laws, which allow for a reduced rib exposure whilst (partially) restoring focal point intensity through power compensation. Although such methods provide an excellent means of reducing rib exposure, they generally increase the local energy density in the pre-focal area, which similarly can lead to undesired overheating. Therefore, this numerical study aimed at evaluating whether a novel transducer design could provide improvement for intercostal HIFU applications, in particular with respect to the pre-focal area. Methods: A combination of acoustic and thermal simulations was used to evaluate 2 mono-element transducers, 2 clinical phased array transducers, and 4 novel transducers based on Fermat’s Spiral (FS), two of which were Voronoi-tessellated (VTFS). Binary apodizations were determined for the phased array transducers using a collision detection algorithm. A tissue geometry was modeled to represent an intercostal HIFU sonication in the liver at 30 and 50 mm behind the ribs, including subsequent layers of gel pad, skin, subcutaneous fat, muscle, and liver tissue. Acoustic simulations were then conducted using propagation of the angular spectrum of plane waves (ASPW). The results of these simulations were used to evaluate pre-focal intensity levels. Subsequently, a finite difference scheme based on the Pennes bioheat equation was used for thermal simulations. The results of these simulations were used to calculate both the energy density in the pre-focal skin, fat, and muscle layers, as well as the energy exposure of the ribs. Results: The acoustic simulations showed that for a sonication in a single point without beamsteer-ing, comparing the best performing clinical phased array in this study to an equivalent VTFS trans-ducer, the maximum intensity in the focal point was increased from 19.0 to 27.0 W/mm² for the sonication 30 mm behind the ribs, while the rib area exposed to ≥20 J/cm² was reduced from 0.88 to 0.14 cm². For the sonication 50 mm behind the ribs, the maximum focal point intensity was increased from 13.4 to 21.5 W/mm², while the rib area exposed to ≥40 J/cm² was lowered from 2.71 to 0.01 cm². The thermal simulations showed that for a circular sonication cell of 4 mm diameter in the transversal plane, sonication times for sonications 30/50 mm behind the ribs were reduced from 13.9 to 8.38 s/38.2 to 17.4 s, respectively. Energy density levels in the skin for these sonications were decreased from 5.28 to 2.22/9.45 to 3.78 J/mm². Conclusions: VTFS transducers are expected to provide improvement for intercostal HIFU applications compared to currently available clinical transducers, as they reduce both the energy density in the pre-focal zone and the energy exposure of the ribs. These characteristics allow for increasing either the re-sonication rate or the treatment volume per sonication.