Calculating the Effect of Ribs on the Focus Quality of a Therapeutic Spherical Random Phased Array

The overlaying rib cage is a major hindrance in treating liver tumors with high intensity focused ultrasound (HIFU). The problems caused are overheating of the ribs due to its high ultrasonic absorption capability and degradation of the ultrasound intensity distribution in the target plane. In this work, a correction method based on binarized apodization and geometric ray tracing approach was employed to avoid heating the ribs. A detailed calculation of the intensity distribution in the focus plane was undertaken to quantify and avoid the effect on HIFU beam generated by a 1-MHz 256-element random phased array after the ultrasonic beam passes through the rib cage. Focusing through the ribs was simulated for 18 different idealized ribs-array configurations and 10 anatomically correct ribs-array configurations, to show the effect of width of the ribs, intercostal spacing and the relative position of ribs and array on the quality of focus, and to identify the positions that are more effective for HIFU applications in the presence of ribs. Acoustic simulations showed that for a single focus without beam steering and for the same total acoustic power, the peak intensity at the target varies from a minimum of 211 W/cm² to a maximum of 293 W/cm² for a nominal acoustic input power of 15 W, whereas the side lobe level varies from 0.07 I_peak to 0.28 I_peak and the separation between the main lobe and side lobes varies from 2.5 mm to 6.3 mm, depending on the relative positioning of the array and ribs and the beam alignment. An increase in the side lobe level was observed by increasing the distance between the array and the ribs. The parameters of focus splitting and the deterioration of focus quality caused by the ultrasonic propagation through the ribs were quantified in various possible different clinical scenarios. In addition to idealized rib topology, anatomical realistic ribs were used to determine the focus quality of the HIFU beam when the beam is steered both in axial and transverse directions and when the transducer is positioned at different depths from the rib cage.