1. A method for characterizing a tissue volume of a patient, comprising: scanning the tissue volume with a ring transducer comprising a set of transmitters configured to emit acoustic waves towards the tissue volume and a set of receivers configured to detect a plurality of acoustic waves from the tissue volume; at a computer processing system in communication with the ring transducer, receiving an acoustic dataset derived from the plurality of acoustic waves; at the computer processing system, generating a set of renderings of the tissue volume from the acoustic data set, wherein the set of renderings includes a first rendering representing a distribution of acoustic speed, a second rendering representing a distribution of acoustic attenuation, and a third rendering representing a distribution of acoustic reflection within the tissue volume; at the computer processing system, generating a merged rendering from the first, the second, and the third renderings; at the computer processing system, identifying a region of interest within the tissue volume from the merged rendering; at the computer processing system, determining a set of prognostic parameters for the region of interest, wherein the set of prognostic parameters includes an attenuation value, a speed value, and a reflection index characterizing margin sharpness for the region of interest and derived from changes in acoustic impedance within the region of interest; and at the computer processing system, outputting an analysis of the region of interest derived from the set of prognostic parameters, the analysis indicative of presence of cancer within the tissue volume.