Heating of biological tissues by two-dimensional phased arrays with random and regular element distributions

The effect of an irregularity of the element distribution in a two-dimensional phased array upon the efficiency of heating of biological tissue is studied in an ultrasonic surgery regime. Two arrays of 256 piston elements, which either form a regular square pattern or are positioned randomly on the surface of a spherical segment, are considered as a model. The formation and the steering of a set of nine foci along the array axis and in the direction perpendicular to it are investigated. The theoretical model includes the algorithm of determining a phase set at the array elements that is optimal for the formation of foci with equal intensities and a preset geometry, as well as the calculation of acoustic and temperature fields in a tissue. The results of numerical simulation are presented for the spatial distributions of ultrasonic intensity, temperature, and the corresponding thermal dose in tissue. It is demonstrated that an irregularity of the element distribution reduces the level of secondary intensity peaks in the field produced by the array. This provides an opportunity to avoid the overheating and ablation of tissue outside the target volume, even in the case of steering with the set of foci away from the array axis within a distance of ±7 mm. A nine-foci regime is studied with the parameters necessary to produce uniform thermal ablation in a volume that is evaluated on the basis of the thermal dose distribution.