The classical "Bio Heat Transfer Equation (BHTE)" model is adapted to take into account the effects of oscillating microbubbles that occur naturally in the tissue during high-intensity focused ultrasound (HIFU) treatment. First, the Gilmore-Akulichev model is used to quantify the acoustic pressure scattered by microbubbles submitted to HIFU. Because this scattered pressure is not monochromatic, the concept of harmonic attenuation is introduced and a global attenuation coefficient is estimated for bubble-filled tissues. The first results show that this global attenuation coefficient varies significantly with respect to several parameters such as the frequency and the density of microbubbles in the medium, but also with respect to the incident acoustic pressure which thus becomes a transcendental function. Under these conditions, a layer-by-layer modeling, in the direction of propagation, is proposed to calculate the ultrasonic beam. Finally, the BHTE is solved and the HIFU-induced lesions are estimated by the calculation of the thermal dose. Using this model, it can be observed first that, when the firing power increases, the lesion develops clearly in the direction of the transducer, with a shape agreeing with in vivo experimentation. Next, it is observed that the lesion can be significantly modified in size and position, if an interface (skin or inner wall) is simulated as a zone with multiple cavitation nuclei. With a firing power increase, it is also shown how a secondary lesion can appear at the interface and how, beyond a certain threshold, this lesion develops at the main lesion expense. Finally, a better in-depth homogeneity of lesions is observed when the acoustic frequency of HIFU is increased.
A time-domain numerical model is presented for simulating the finite-amplitude focused acoustic pulse propagation in a dissipative and nonlinear medium with a symmetrical source geometry. In this method, the main effects responsible in finite-amplitude wave propagation, i.e., diffraction, nonlinearity, and absorption, are taken into account. These effects are treated independently using the method of fractional steps with a second-order operator-splitting algorithm. In this method, the acoustic beam propagates, plane-by-plane, from the surface of a highly focused radiator up to its focus. The results of calculations in an ideal (linear and nondissipative) medium show the validity of the model for simulating the effect of diffraction in highly focused pulse propagation. For real media, very good agreement was obtained in the shape of the theoretical and experimental pressure-time waveforms. A discrepancy in the amplitudes was observed with a maximum of around 20%, which can be explained by existing sources of error in our measurements and on the assumptions inherent in our theoretical model. The model has certain advantages over other time-domain methods previously reported in that it: (1) allows for arbitrary absorption and dispersion, and (2) makes use of full diffraction formulation. The latter point is particularly important for studying intense sources with high focusing gains.
The ions of solutions exposed to the propagation of ultrasound in the presence of a magnetic field experience Lorentz force. Their movement gives rise to a local electric current density, which is proportional to the electric conductivity of the medium. In vitro assessment of this current is performed using simple models of biological media. A constant magnetic field of 0.35 T and 500 kHz pulsed ultrasound are used. The sensing electrodes are exposed to neither the pressure wave nor the magnetic field, thus ensuring that the signal is not due to any undesirable electrode effect. The experimental results confirm that the current is proportional to the electrical conductivity of the medium. The changes in the measured current against the width of the measurement chamber show that the electrodes only collect a fraction of the current created within the medium. The magnitude of the measured current is 50nA in a saline solution of 0.5 S/m conductivity. The technique enabled the determination of the conductivity of a porcine blood sample against haematocrit. It is concluded that this type of measurement has the potential to allow the electrical conductivity of a medium to be determined using ultrasound.
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