An implantable device includes a first sealed flexible shell configured for implantation within a breast of a human subject, an elastic filler material contained within the first sealed flexible shell, a second sealed flexible shell, which is disposed within the elastic filler material inside the first sealed flexible shell and a volume of gas contained within the second sealed flexible shell, such that the volume of the gas is less than a threshold inflation volume required to induce a non-zero strain in the second sealed flexible shell when the device is subject to an external pressure of one atmosphere.