A medical valve implant comprising: an implant structure configured as a medical valve; and a base body that includes a collar extending in a circumferential direction around the implant structure, wherein the collar includes a first cell structure composed of a plurality of cells forming an inner cross section of the base body that is matched to an outer cross section of the implant structure, characterized in that the collar includes a second cell structure fastened to an inner contour of a cell of the first cell structure at two fastening points and configured to move radially outward relative to the first cell structure so that an outer contour of the base body is formed by the first cell structure and the second cell structure.