Design aspects of focal beams from high-intensity arrays

Abstract

As the applications of ultrasonic thermal therapies expand, the design of the high-intensity array must address both the energy delivery of the main beam and the character and relevance of off-target beam energy. We simulate the acoustic field performance of a selected set of circular arrays organized by array format, including flat versus curved arrays, periodic versus random arrays, and center void diameter variations. Performance metrics are based on the −3-dB focal main lobe (FML) positioning range, axial grating lobe (AGL) temperatures, and side lobe levels. Using finite-element analysis, we evaluate the relative heating of the FML and the AGLs. All arrays have a maximum diameter of 100λ, with element count ranging from 64 to 1024 and continuous wave frequency of 1.5 MHz. First, we show that a 50% spherical annulus produces focus beam side lobes which decay as a function of lateral distance at nearly 87% of the exponential rate of a full aperture. Second, for the arrays studied, the efficiency of power delivery over the −3-dB focus positioning range for spherical arrays is at least 2-fold greater than for flat arrays; the 256-element case shows a 5-fold advantage for the spherical array. Third, AGL heating can be significant as the focal target is moved to its distal half-intensity depth from the natural focus. Increasing the element count of a randomized array to 256 elements decreases the AGL-to-FML heating ratio to 0.12 at the distal half-intensity depth. Further increases in element count yield modest improvements. A 49% improvement in the AGL-to-peak heating ratio is predicted by using the Sumanaweera spiral element pattern with randomization.

Development of a spherically focused phased array transducer for ultrasonic image-guided hyperthermia

“…In addition, the simulations show that the current array has a FPI of 2077 W/cm 2 at the geometric focus and 2109 W/cm 2 at (0, 0, 53.5) mm given the surface intensity of the array elements being 1 W/cm 2 . The intensity gain (2077) at the geometric focus obtained in this simulation differs by 0.1% from the theoretical estimate obtained according to the following equation (Oneil 1949, Stephens et al 2011): $$G_I\cong {\left(\frac{N\pi r^2}{\lambda R_c}\right)}^2{e}^{-0.2303{\alpha }_m{R}_c}$$ where N is the number of elements, r is the radius of the circular element, λ is the wavelength, R c is the radius of curvature of the array in cm, and α m is the absorption characteristics of the medium in unit of dB/cm.…”

In situ bone tissue engineering via ultrasound-mediated gene delivery to endogenous progenitor cells in mini-pigs

“…For efficient gene delivery using our proposed therapy, imaging provides the opportunity to ensure sufficient sonoporation despite the fixation plates that have the potential to impede the ultrasonic waves. More robust ultrasound systems can be implemented to bypass these hurdles in future human therapies (55). …”

Flexible integration of high-imaging- resolution and high-power arrays for ultrasound-induced thermal strain imaging (US-TSI)

“…By combining the geometry of a spherical aperture [15] and previously described optimal depth calculations [16], [17] the optimal operating frequency for a spherical aperture can be found. We examined the highly curved spherical aperture with kh > 4.…”

“…Using previously described methods [17], [19], the Rayleigh-Sommerfeld (RS) equation was used to obtain a combined volumetric pressure field for the 6 elements. With regards to the flat aperture beam modeling, it is expected that a single beam focus will occur at depth z = D 2 /4λ with a focal intensity of four times the aperture surface pressure and a full width half power beam (FWHP) angle of approximately λ/D.…”