In this paper, we present a novel design framework of synthetic radial aperture focusing for 3-dimensional (3-D) transrectal ultrasound imaging (TRUS-rSAF), in which multiple transmittance/reception events at different scanning angles are synthesized to reconstruct a radial plane in the target volume, securing high spatial resolution and texture uniformity. A theory-based design approach has not been available to push the envelope of the 3-D rSAF technique. Herein, a closed-form analytical description of the TRUS-rSAF method is presented for the first time, effectively delineating spatial resolution and grating lobe positions in the radial dimension of a TRUS transducer. We demonstrate a solid optimization workflow based on the theoretical foundation to improve its spatiotemporal resolution, grating lobe artifacts, and signal-to-noise ratio (SNR). A specific design criterion was considered to outperform a clinical 3-D TRUS imaging (TRUS-REF), where each radial plane is reconstructed with a single transmittance/reception event using a motorized actuator. The optimized TRUS-rSAF method significantly enhanced spatial resolution up to 50 % over the TRUS-REF method while providing clinically-effective temporal resolution (2-8 volumes per second) with negligible grating lobe artifacts. The results indicate that the proposed design approach would enable a novel TRUS imaging solution in clinics.
