Numerical simulation of volumetric ultrasound heating of biological tissue with surface cooling

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One of the undesirable effects of using ultrasound for extracorporeal therapy is skin overheating, caused by both ultrasound absorption and contact with the heated surface of the acoustic transducer. To suppress this effect, a forcibly cooled contact medium can be placed between the skin and the irradiating surface. A novel ultrasonic applicator implementing this approach has recently been proposed and developed at SFU. It uses a rectangular piezoelectric transducer bonded to an aluminum plate for volumetric heating of subcutaneous biotissue. The plate is cooled by circulating cold water through laterally drilled channels. This paper presents a numerical algorithm for calculating the three-dimensional temperature field in the tissue during the operation of this applicator. The simulation was based on the inhomogeneous heat equation. Experimental acoustic holography data obtained for the developed transducer were used to calculate the heat sources in the tissue. An example of heating bovine liver tissue ex vivo is considered, with irradiation times ranging from several seconds to several minutes. The simulation results were compared with experimental data on tissue thermal ablation at an acoustic power of 12 W and an ultrasound frequency of 6.96 MHz. It is shown that the combination of thermal tissue exposure and contact boundary cooling allows for volumetric tissue heating with a temperature maximum at a depth of 8 to 15 mm, while maintaining a negligible temperature change at depths up to 2–3 mm.

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作者简介

P. Pestova

Moscow State University

编辑信件的主要联系方式.
Email: pestova.pa16@physics.msu.ru

физический факультет

俄罗斯联邦, Moscow, 119991

A. Rybyanets

Research Institute of Physics

Email: pestova.pa16@physics.msu.ru
俄罗斯联邦, Rostov on Don, 344090

O. Sapozhnikov

Moscow State University

Email: pestova.pa16@physics.msu.ru

физический факультет

俄罗斯联邦, Moscow, 119991

M. Karzova

Moscow State University

Email: pestova.pa16@physics.msu.ru

физический факультет

俄罗斯联邦, Moscow, 119991

P. Yuldashev

Moscow State University

Email: pestova.pa16@physics.msu.ru

физический факультет

俄罗斯联邦, Moscow, 119991

S. Tsysar

Moscow State University

Email: pestova.pa16@physics.msu.ru

физический факультет

俄罗斯联邦, Moscow, 119991

L. Kotelnikova

Moscow State University

Email: pestova.pa16@physics.msu.ru

физический факультет

俄罗斯联邦, Moscow, 119991

I. Shvetsov

Research Institute of Physics

Email: pestova.pa16@physics.msu.ru
俄罗斯联邦, Rostov on Don, 344090

V. Khokhlova

Moscow State University

Email: pestova.pa16@physics.msu.ru
俄罗斯联邦, Moscow, 119991

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2. Fig. 1. (a) — Schematic diagram of the numerical experiment simulating the physical experiment ex vivo. A flat ultrasonic emitter, which is a glued rectangular piezoelectric plate (PP) and an aluminum plate (AP) with channels along its lateral sections (LS), was applied to a sample of beef liver with an initial temperature of 23°C. The AP was thermostatted by circulating cold water with a temperature of 14°C through its channels. The spatial distribution of the ultrasonic field pressure amplitude in the tissue is shown inside the sample. (b) — Front view and dimensions of the piezoelectric plate (PP is shown in brown) and the cooling plate (AP is shown in gray). The numerical window is shown in blue.

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3. Fig. 2. Boundary conditions on the surface of the emitter (the outer surface of the aluminum plate) at z = 0, used to model the ultrasonic field created in the tissue: distributions of (a) the amplitude and (b) the phase of the pressure for an acoustic power of the emitter of 12 W. The dashed lines show the nominal dimensions of the piezoelectric plate 2.5 × 1.5 cm.

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4. Fig. 3. Spatial distributions of the pressure amplitude in water in two axial planes xz (upper row) and yz (lower row) at a frequency of 6.96 MHz for an acoustic power of the emitter of 12 W. The distributions are calculated (a) based on acoustic holography data for the emitter under consideration and (b) for an ideal piston emitter with nominal dimensions.

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5. Fig. 4. Numerically calculated spatial distributions of the pressure amplitude in the tissue in the axial planes (a) — xz, (b) — yz for a frequency of 6.96 MHz and an acoustic power of the emitter of 12 W.

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6. Fig. 5. Spatial distribution of the power density of thermal antisymmetric sources Q in the tissue in the axial planes (a) — xz and (b) — yz at an operating frequency of 6.96 MHz for an emitter power of 12 W.

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7. Fig. 6. Spatial distributions of temperature in the tissue (a) — at time t = 60 s after switching on sample cooling and (b) — after establishing a stationary temperature distribution at time t = 80 min. (c) — Dependences of sample temperature T on time t on the emitter axis for characteristic depths: 3 cm (blue curve), 1.5 cm (red curve), 0.2 cm (yellow curve).

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8. Fig. 7. Spatial temperature distributions in axial planes (a, c) — xz and (b, d) — yz at the end of irradiation of a beef liver sample with a combination of heating and cooling. The tissue irradiation time was (a, b) — t = 3 min and (c, d) — t = 5 min. The white contour shows the region within which the thermal dose exceeded the threshold value after the sample had cooled for 2 min.

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9. Fig. 8. Results of comparison of the results of (a, c) — numerical and (b, d) — physical experiments on irradiation of beef liver tissue ex vivo for an acoustic power of 12 W and an irradiation time of (a, b) — 3 min and (c, d) — 5 min.

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