Effect of the diameter of central opening on nonlinear acoustic field characteristics of high-intensity focused ultrasound transducers

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Abstract

A number of novel non-invasive surgical technologies utilizing high-intensity focused ultrasound (HIFU) are based on the exploitation of nonlinear acoustic effects, leading to wave profile distortion and formation of shock fronts at the focus. Typically, these systems consist of multiple, nearly axially symmetric transducers creating a powerful ultrasound beam, with a central circular opening for accommodating a diagnostic probe for visualization purposes. For predicting focal field parameters for such transducer geometries, the equivalent source model of a spherical segment is convenient, as nonlinear effects in its field are well-studied. The equivalent source parameters (diameter, focal length, and amplitude) are optimized to closely approximate the axial focal region of the original transducer. This work investigates the influence of central opening size on nonlinear field characteristics and the applicability of the equivalent source model for a typical therapeutic ultrasound transducer with a frequency of 1 MHz and F# = 0.9. It is demonstrated that the central opening size significantly affects the manifestation of nonlinear effects in the focal region, and the equivalent source model can be applied only when the opening diameter is less than 20% of the transducer diameter.

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About the authors

F. A. Nartov

Lomonosov Moscow State University

Author for correspondence.
Email: nartov.fyodor@gmail.com

Faculty of Physics

Russian Federation, Leninskie Gory 1, Moscow, 119991

M. M. Karzova

Lomonosov Moscow State University

Email: nartov.fyodor@gmail.com

Faculty of Physics

Russian Federation, Leninskie Gory 1, Moscow, 119991

V. A. Khokhlova

Lomonosov Moscow State University

Email: nartov.fyodor@gmail.com

Faculty of Physics

Russian Federation, Leninskie Gory 1, Moscow, 119991

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Supplementary files

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2. Fig. 1. (a) — Model of a spherical emitter with F# = 0.9 (side view); models of spherical emitters with different sizes of central holes (frontal view): (b) — 0, (c) — 40, (d) — 70 mm.

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3. Fig. 2. Distributions of the normalized pressure amplitude along the acoustic axis in a linear beam for a radiator with a central hole of 40 mm in diameter: black is the original radiator, red is the equivalent source.

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4. Fig. 3. Distributions of normalized pressure amplitudes in the axial plane in the focal region in the linear propagation mode for emitters with different central holes and equivalent sources. (a) — Emitter without a hole; upper row (b, d) — fields of the original emitters, lower row (c, d) — sources equivalent to them. Hole diameters: (a) — 0, (b, c) — 40, (d, d) — 70 mm.

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5. Fig. 4. Saturation curves: dependences of peak positive and negative pressures (solid lines) and shock front amplitude (dashed line) on the emitter power for different aperture sizes: red - 0, blue - 40, black - 70 mm. The points on the curves correspond to the conditions for the formation of a developed discontinuity in the focal profile of the wave. The dashed lines show the corresponding dependences of the wave amplitude at the focus in the linear beam.

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6. Fig. 5. One period of the wave profile at the focus for emitters with different aperture sizes: red — 0, blue — 40, black — 70 mm, and different focusing modes: (a) — in the quasi-linear mode (10% of the wave energy in higher harmonics); (b) — in the mode of formation of a developed discontinuity (when the lower boundary of the shock front corresponds to zero pressure, Ash = p+); (c) — in the saturation mode.

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7. Fig. 6. Distributions of peak positive (top row) and negative (bottom row) pressures in the plane of the beam axis during the formation of a developed rupture (Ash = p+) for different hole diameters: left column - 0, middle column - 40, right column - 70 mm.

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8. Fig. 7. Comparison of ultrasonic field characteristics for emitters with a central hole (purple curves) and for equivalent emitters (green curves) for different hole diameters: (a, g, f) — 10, (b, e, h) — 40 and (c, f, i) — 70 mm. Top row — axial distributions of normalized pressure amplitudes in the linear beam. Middle row — transverse distributions of normalized pressure amplitudes in the focal plane of the linear beam. Bottom row — saturation curves of peak positive and negative pressures at the focus; points on the curves correspond to the formation of a developed discontinuity in the focal profile of the wave.

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9. Fig. 8. Dependences of peak positive and negative pressures at the focus on the diameter of the central hole for the original emitters (blue curves) and for the corresponding equivalent emitters (red curves) for different focusing modes: (a) — in the quasi-linear mode; (b) — in the mode of formation of a developed discontinuity; (c) — in the saturation mode (the amplitude of the discontinuity is shown by the dotted line).

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