Final answer:
The shadowing posterior to each lateral border of the breast cyst in ultrasound imaging is caused by the redirection of the sound beam at an interface with different propagation speeds and a curved surface.
Step-by-step explanation:
The source of the shadowing posterior to each lateral border of the breast cyst in the ultrasound imaging is option A: redirection of the sound beam at an interface with different propagation speeds and a curved surface.
When the ultrasound beam encounters the interface between the cyst and the surrounding tissue, it is redirected and scattered due to the different propagation speeds and curved surface of the cyst.
This redirection of the sound beam causes shadowing posterior to each lateral border of the cyst, resulting in a dark area on the ultrasound image.