Modeling of Tissues in vivo Heating Induced by Exposure to Therapeutic Ultrasound

Abstract

The aim of this work is mathematical modeling and numerical calculation in space and time of temperature fields induced by low power focused ultrasound beams in soft tissue in vivo after few minutes exposure time. These numerical predictions are indispensable for planning of various ultrasound therapeutic applications. Both, the acoustic pressure distribution and power density of heat sources induced in tissue, were calculated using the numerical solution to the second order nonlinear differential wave equation describing propagation of the high intensity acoustic wave in three-layer structure of nonlinear attenuating media. The problem of the heat transfer in living tissues is modelled by the Pennes equation, which accounts for the effects of heat diffusion, blood perfusion losses and metabolism rate. Boundary conditions and geometry are chosen according to the anatomical dimensions of a rat liver. The obtained results are compared with those calculated previously and verified experimentally for temperature elevations induced by ultrasound in liver samples in vitro. The analysis of the results emphasizes the value of the blood perfusion and the values of heat conductivity on the temperature growth rate. The numerical calculations of temperature fields were performed using the ABAQUS FEM software package. The thermal and acoustic properties of the liver and water being the input parameters to the numerical model were taken from the published data in cited references. The range of thermal conductivity coefficient of living tissue is obtained from the model of two-phase composite medium with given microstructure. The first component is a "solid" tissue and the second one corresponds to blood vessels area. The circular focused ultrasonic transducer with a diameter of 15 mm, focal length of 25 mm and resonance frequency of 2 MHz has been used to generate the pulsed ultrasonic beam in a very introductory experiment in vivo, which has been performed. Numerical prediction confirms qualitatively its results.

Temperature Monitoring during Focused Ultrasound Treatment by Means of the Homodyned K Distribution

“…Phantom had cylindrical shape of diameter and height of 5 cm and 9 cm, respectively. The sample was positioned in a tank filled with temperature-controlled degassed distilled water [20,21]. Figure 1 shows the experimental setup which includes a generator (Agilent 332, Aprings Colorado, USA), an amplifier (ENI 1325LA, Rochester NY, USA), and an oscilloscope (Tektronix TDS3012B).…”

“…The average power of focused ultrasound beam was 6 W. The focal zone was set at a depth of 30 mm within the phantom. A more comprehensive description of the experimental setup can be found in [20,21].…”

Bulletin of the Polish Academy of Sciences: Technical Sciences

“…This increase is the most sensitive to variations of thermal conductivity, cf. [41]. Figure 9 showed the curve of temperature/time dependence during ultrasonic irradiation of the MNP16 sam- Ultrasonic specific absorption rate was the assessment of the goodness of fit of the temperature increase measured and calculated at the time of sonication less than 15 s. In Fig.…”