The utility of sparse 2D fully electronically steerable focused ultrasound phased arrays for thermal surgery: A simulation study

Sparse arrays are widely used in diagnostic ultrasound for their strong performance and relative technical simplicity. This simulation study assessed the efficacy of phased arrays of varied sparseness for thermal surgery, especially with regard to power consumption and near-field heating. It employs a linear ultrasound propagation model and a semi-analytical solution to the Pennes' bioheat transfer equation. The basic design had 4912 cylindrical transducers (500 kHz) arranged on a flat 12 cm disk (1.5 mm spacing). This array was compared to randomly-thinned sparse arrays with 75%, 50% and 25% populations. Temperature elevations of 60 and 70 °C were induced in sonication times of 5-20 s, at foci spanning depths of 50-150 mm and radii of 0-60 mm. The sparse arrays produced nearly indistinguishable focal patterns but, averaged across the foci, required 132%, 200% and 393% of the power of the full array, respectively, applied through fewer transducer elements. Comparable results were found at 1 MHz from equivalent arrays. Simulated lesions were formed (thermal dose ≥ 240 equivalent minutes at 43 °C (T₄₃)) and 'transition' and 'unsafe' regions (both defined as 5 min < T₄₃ < 240 min) were identified, the former immediately surrounding the lesion and the latter anywhere else. At a depth of 100 mm, sparse arrays were found to produce comparable lesions to the full array at the focus, but 'unsafe', over-heated near-field regions after some ablated lesion volume: about 12 mL for the 25% array, around 100 mL for the 50% array, while the 75% and full arrays produced 150 mL lesions safely.