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Computer modeling of spherical-section phased arrays for ultrasound surgery (tissue ablation) is described. The influence on performance of the number of circular elements (68 to 1024), their diameter (2.5 to 10 mm), frequency (1 to 2 MHz), and degree of sparseness in the array is investigated for elements distributed randomly or in square, annular, and hexagonal patterns on a spherical shell (radius of curvature, 120 mm). Criteria for evaluating the quality of the intensity distributions obtained when focusing the arrays both on and away from their center of curvature, and in both single focus and simultaneous multiple foci modes, are proposed. Of the arrays studied, the most favorable performance, for both modes, is predicted for 256 5-mm diameter, randomly distributed elements. For the single focus mode, this performed better than regular arrays of 255 to 1024 elements and, for the case of nine simultaneous foci produced on a coplanar 3/spl times/3 grid with 4-mm spacing, better than square, hexagonal, or annular distributed arrays with a comparable number of elements. Randomization improved performance by suppressing grating lobes significantly. For single focus mode, a several-fold decrease in the number of elements could be made without degrading the quality of the intensity distribution.