Edge shadows around rigid, absorbing, and nonabsorbing cylinders

Edge shadows are often observed on images of rounded cavities, such as cysts, as narrow dark lines, aligned with the ultrasound beam, and extending distally from the cavity edges. We hypothesised that the acoustic properties of the cavity material are ´encoded´ in the appearance of these shadows, and so could be revealed by an increased understanding of their physical origins. As a step toward this, we have investigated the relative importance, in edge shadow generation, of the part of the beam transmitted through the cavity, to that which remains outside. We have developed a pulsed, finite beam wave equation solution to simulate images of liquid cylindrical cavities embedded in tissue-mimicking material (TMM). Using this, we investigated the production of edge shadows around cylinders with ±10% speed of sound (SOS) relative to the TMM, when insonated with a strongly focussed beam. The main criterion used to assess the significance of transmission through the cylinder was the proportion of the pulse-echo sensitivity within the cylinder, relative to that outside. The effect on the images of the presence or absence of absorption, and of scattering centres, within the cylinder was also studied. The images of these penetrable cylinders were then compared to those of rigid and evacuated cylinders, for neither of which could energy be penetrating into the cylinder. Edge shadows in the +10% SOS case have two parts, and are qualitatively different to those in the -10% case. On the +10% SOS cylinder, the beam corresponding to the part of the shadow immediately beneath the edge of the cylinder remained almost totally outside the cylinder with at most 23% of the pulse-echo sensitivity inside the cylinder. In contrast, transmission through the cylinder was much more important for the beam producing that part of the shadow lying beneath the critical angle, with up to 74% of the sensitivity lying within the cylinder. For the -10% SOS case, with no critical angle, only the shadow beneath the cylinder edge was present. Again, significant transmission into the cylinder was occurring, but less than at the critical angle, with up to 40% of the sensitivity within the cylinder. Inclusion of absorption of 0.5dB/cm/MHz within the cylinder appeared simply to darken only- those parts of the images which had, according to the sensitivity criterion, involved significant penetration into the cylinder. Inclusion of scatterers within the cylinder had negligible effect on the image intensity distal to the cylinders, indicating that little energy was ´trapped´ within the cylinder. The images of the rigid and evacuated cylinders were very similar to each other. However, the edge shadow on the rigid cylinder was significantly darker than that on either of the penetrable cylinders.