A prosthetic mitral valve apparatus configured to be deployed within a native mitral valve of a mammalian heart, the prosthetic mitral valve apparatus comprising: a prosthetic heart valve mechanism comprising at least a valve member that is configured to restrict blood flow from a left ventricle to a left atrium of the mammalian heart; a valve frame defining a frame aperture, said frame aperture sized to: circumferentially enclose the prosthetic heart valve mechanism, and fit within an aperture of the native mitral valve, between the left ventricle and the left atrium of the mammalian heart; and at least one arm attached to a portion of the valve frame on a ventricular side of said frame aperture, the at least one arm being configured to extend radially from the portion of the valve frame such that: a chord receiving surface of the arm is sized and shaped to deploy among a region of the chords of the native mitral valve, and the arm is curved, with an interior of the arm facing a direction in which the valve frame is configured to be rotated during deployment of the prosthetic mitral valve apparatus within the native mitral valve and with the arm having a concavely rounded leading edge facing in a circumferential direction, such that upon the valve frame being rotated in said direction, the arm is configured to deflect the shape of contacted chords, to thereby pull at least one valve leaflet of the native mitral valve at least partially around said frame aperture, and into an at least partially closed configuration around said frame aperture. a prosthetic heart valve mechanism comprising at least a valve member that is configured to restrict blood flow from a left ventricle to a left atrium of the mammalian heart; a valve frame defining a frame aperture, said frame aperture sized to: circumferentially enclose the prosthetic heart valve mechanism, and fit within an aperture of the native mitral valve, between the left ventricle and the left atrium of the mammalian heart; and circumferentially enclose the prosthetic heart valve mechanism, and fit within an aperture of the native mitral valve, between the left ventricle and the left atrium of the mammalian heart; and at least one arm attached to a portion of the valve frame on a ventricular side of said frame aperture, the at least one arm being configured to extend radially from the portion of the valve frame such that: a chord receiving surface of the arm is sized and shaped to deploy among a region of the chords of the native mitral valve, and the arm is curved, with an interior of the arm facing a direction in which the valve frame is configured to be rotated during deployment of the prosthetic mitral valve apparatus within the native mitral valve and with the arm having a concavely rounded leading edge facing in a circumferential direction, such that upon the valve frame being rotated in said direction, the arm is configured to deflect the shape of contacted chords, to thereby pull at least one valve leaflet of the native mitral valve at least partially around said frame aperture, and into an at least partially closed configuration around said frame aperture. a chord receiving surface of the arm is sized and shaped to deploy among a region of the chords of the native mitral valve, and the arm is curved, with an interior of the arm facing a direction in which the valve frame is configured to be rotated during deployment of the prosthetic mitral valve apparatus within the native mitral valve and with the arm having a concavely rounded leading edge facing in a circumferential direction, such that upon the valve frame being rotated in said direction, the arm is configured to deflect the shape of contacted chords, to thereby pull at least one valve leaflet of the native mitral valve at least partially around said frame aperture, and into an at least partially closed configuration around said frame aperture.