title: Frequency considerations for deep ablation with high-intensity focused ultrasound: A simulation study.
abstract: OBJECTIVE
  The objective of this study was to explore frequency considerations for large-volume, deep thermal ablations with focused ultrasound. Though focal patterns, focal steering rate, and the size of focal clusters have all been explored in this context, frequency studies have generally explored shallower depths and hyperthermia applications. This study examines both treatment efficiency and near-field heating rate as functions of frequency and depth.
  
  
  METHODS
  Flat, 150 mm transducer arrays were simulated to operate at frequencies of 250, 500, 750, 1000, 1250, and 1500 kHz. Each array had λ2 interelement spacing yielding arrays of 2000-70 000 piston-shaped elements arranged in concentric rings. Depths of 50, 100, and 150 mm were explored, with attenuation (α) values of 2.5-10 (Np/m)/MHz. Ultrasound propagation was simulated with the Rayleigh-Sommerfeld integral over a volume of homogeneous simulated tissue. Absorbed power density was determined from the acoustic pressure which, in turn, was modeled with the Pennes bioheat transfer equation. Using this knowledge of temperature over time, thermal dose function of Sapareto and Dewey was used to model the resulting bioeffect of each simulated sonication. Initially, single foci at each depth, frequency, and α were examined with either fixed peak temperatures or fixed powers. Based on the size of the resulting, single foci lesions, larger compound sonications were designed with foci packed together in multiple layers and rings. For each depth, focal patterns were chosen to produce a similar total ablated volume for each frequency. These compound sonications were performed with a fixed peak temperature at each focus. The resulting energy efficiency (volume ablated per acoustic energy applied), near-field heating rate (temperature increase in the anterior third of the simulation space per unit volume ablated), and near- and far-field margins were assessed.
  
  
  RESULTS
  Lesions of comparable volume were created with different frequencies at different depths. The results reflect the interconnected nature of frequency as it effects focal size (decreasing with frequency), peak pressure (generally increasing with frequency), and attenuation (also increasing with frequency). The ablation efficiency was the highest for α = 5 (Np/m)/MHz at a frequency of 750 kHz at each depth. For α = 10 (Np/m)/MHz, efficiency was the highest at 750 kHz for a depth of 50 mm, and 500 kHz at depths of 100 and 150 mm. At all sonication depths, near-field heating was minimized with lower frequencies of 250 and 500 kHz.
  
  
  CONCLUSIONS
  Large-volume ablations are most efficient at frequencies of 500-750 kHz at depths of 100-150 mm. When one considers that near-field heat accumulation tends to be the rate limiting factor in large-volume ablations like uterine fibroid surgery, the results show that frequencies as low as 500 kHz are favored for their ability to reduce heating in the near-field.
authors.affiliation: Sunnybrook Research Institute, Toronto, Ontario M4N 3M5, Canada and Department of Medical Biophysics, University of Toronto, Toronto, Ontario M5G 1L7, Canada.
authors.forename: Nicholas
authors.initials: N
authors.lastname: Ellens
authors.affiliation: Sunnybrook Research Institute, Toronto, Ontario M4N 3M5, Canada and Department of Medical Biophysics, University of Toronto, Toronto, Ontario M5G 1L7, Canada.
authors.forename: Kullervo
authors.initials: K
authors.lastname: Hynynen
mesh_terms: D003198:Computer Simulation; D057086:High-Intensity Focused Ultrasound Ablation / Q000379:methods*; D008954:Models, Biological; D011312:Pressure; D013696:Temperature; D000069453:Ultrasonic Waves