# Versatile High-Throughput Platform for Focused Ultrasound In Vitro Application
## 2 Materials and Methods
### Simulation of Different Platform Configurations
#### 2.2.2 High-Intensity Focused Ultrasound (HIFU) Platform  
The HIFU platform was designed to facilitate the application of higher pressures and extended duty cycles in the wells. Because the high-pressure levels required to study effects beyond mild hyperthermia pose significant challenges to individual transducers for each well in a 96-well plate, subset configurations of the plate were studied that could be effectively sonicated simultaneously. To compromise between high pressure and stimulating as many wells as possible, a configuration of 8 \(\times\) 4 cylindrically focusing transducers was chosen. The dimension along the short side of one element (labeled x-dimension in Figure 2a) corresponded to that of one well, while the dimension of the long side (labeled y-dimension in Figure 2a) corresponded to the size of three wells (Figure 2a,b).  
One challenge with this configuration was reducing the overlap of the pressure fields from adjacent elements due to the larger opening angle in the x-dimension. FEM simulations to optimize the geometry were performed on a simplified model (Figure 3) consisting of a stack of eight cylindrical PZT5H ceramic elements with a backing made of a polyurethane material (Obomodulan(r), OBO-Werke, Stadthagen, Germany). Initial optimizations on the stack of eight elements led to a coverage angle of 110\({}^{\circ}\) for the ceramics with an inner cylinder radius of 13.5 mm and a ceramic thickness of 2 mm. A gap of 2.2 mm between adjacent elements was filled with polyurethane. It was assumed that the transducer elements interface with the well plate via water coupling.  
Figure 1: Simulated XZ pressure distribution field for different circular single-element LIFU transducers of diameter 6.5 mm and frequencies 0.5 MHz (**a**), 1.0 MHz (**b**), 1.5 MHz (**c**) and 2.0 MHz (**d**).  
Figure 2: Applicator geometry with 32 cylindrically focusing transducers for sonication in 32 wells of a 96-well plate. (**a**) Projection of acoustic pressure distribution is schematically shown as a semi-transparent overlay on the well plate model; (**b**) Model of one stack of 8 focusing transducers used as input for the FEM simulation.  
In further numeric experiments, we explored the influence of different backing materials (OBO vs. air), piezoceramic materials, and the dimensions of the eight-element stack on the pressure disturbance to refine the configuration. The effect of sound field separators between adjacent transducers to reduce the pressure disturbance is displayed in Figure 3. Of the sound pressure contained in the well above the active transducer, 49% was transmitted to adjacent cells without the presence of separators, whereas this value fell to 30% of the active well when using OBO walls. Due to the requirement for active cooling of the transducer elements when driven at high duty cycles and voltages (determined by thermal simulations), complete acoustic separation in the x-dimension was not possible. A small opening in the separator between adjacent transducers (Figure 3b) allowed the passage of cooling fluid along channels aligned in the x-dimension. The separator (indicated in white) left a gap for water to flow directly above the transducer element surface.  
The final specifications for the two applicator configurations are summarized in Table 1.