Theoretical model of internally cooled interstitial ultrasound applicators for thermal therapy

Abstract

Interstitial ultrasound applicators for high-temperature thermal therapy are currently being developed for treating cancerous and benign disease. Internally cooled, direct-coupled (ICDC) applicators, composed of a segmented array of cylindrical ultrasound transducers, have demonstrated capabilities of producing controllable and conformal heating distributions along the applicator length and angular orientation. In this study, 2D transient acoustic and biothermal models of ICDC applicators were developed using a mixed implicit and explicit finite difference solution with variable node spacing in cylindrical coordinates for enhanced speed, stability and accuracy. The model incorporates dynamic behaviour of acoustic parameters and blood perfusion as a function of temperature and thermal dose. Acoustic intensity distributions were modelled as a composite of measured and theoretical intensity distributions. The shape and time evolution of temperature contours and thermal lesions for 90°, 200° and 360° angularly directional applicators and multi-transducer applicators were modelled for heating durations between 1 and 5 min. Model parameters were selected to match previously reported ex vivo and in vivo studies of 2.2 mm diameter ICDC devices in thigh muscle and liver (15–30 W cm−2 applied power density, 0.5–5 min treatment times, 2.8–3.6 cm diameter thermal lesions). The temperatures and lethal thermal dose (600 EM43 °C) contours calculated using the models were in excellent agreement with temperatures and thermal lesion dimensions (visible coagulation) determined experimentally. The differences between maximum radial depths of coagulation calculated using the r–z and r–θ models were small, less than ∼2 mm for 10–15 mm lesions. There was a strong correlation between the calculated 50 °C contour and the radial, angular and axial lesion dimensions obtained for 3–5 min heating protocols. The models developed in this study have significant application in design studies and potential future use in treatment planning of ICDC interstitial ultrasound thermal therapy.