A medical tissue wrap, for an internal anatomical structure of a mammal is formed by a coiled wall having a circumferential inner end portion and a circumferential outer end portion extending around and overlapping the circumferential inner end portion. The wall thereby defines a longitudinal through-hole for accommodating a portion of the anatomical structure. The circumferential outer end portion is radially spaced-apart from the circumferential inner end portion by a discontinuous spacing in the circumferential direction. The tissue wrap comprises a structural outer surface modification at opposing longitudinal end portions of its wall.