A medical valve (110, 111, 210, 211, 310) comprising: a housing (120, 220) comprising a sidewall (140, 240, 340) and defining a chamber; a connection interface (130, 230) in fluid communication with the chamber, the connection interface (130, 230) being configured to couple with one or more medical devices for infusion of fluid through the medical valve (110, 111, 210, 211, 310) in a distal direction and aspiration of fluid through the medical valve (110, 111, 210, 211, 310) in a proximal direction; a septum (122, 222, 322) coupled to the housing (120, 220), the septum (122, 222, 322) comprising a proximal surface, a distal surface, and a selectively openable closure (174, 274, 374) that extends through a full thickness of the septum (122, 222, 322) between the proximal surface and the distal surface, wherein the closure (174, 274, 374) is positioned within the chamber; and a plurality of projections (144, 244, 444) that extend away from the sidewall (140, 240, 340), each projection (144, 244, 444) comprising a restriction surface (146, 246) at a distal end thereof that is configured to contact the proximal surface of the septum (122, 222, 322) to oppose movement of a restricted portion of the septum (122, 222, 322) in the proximal direction such that an aspiration cracking pressure required to open the closure (174, 274, 374) to permit fluid flow through the septum (122, 222, 322) in the proximal direction exceeds an infusion cracking pressure required to open the closure (174, 274, 374) to permit fluid flow through the septum (122, 222, 322) in the distal direction, wherein the septum (122, 222, 322) further comprises contact regions at which the septum (122, 222, 322) contacts the restriction surfaces (146, 246) of the plurality of projections (144, 244, 444), the contact regions defining the restricted portion of the septum (122, 222, 322) and having a collective total area that represents only a portion of a total area of the restricted portion of the septum (122, 222, 322). a housing (120, 220) comprising a sidewall (140, 240, 340) and defining a chamber; a connection interface (130, 230) in fluid communication with the chamber, the connection interface (130, 230) being configured to couple with one or more medical devices for infusion of fluid through the medical valve (110, 111, 210, 211, 310) in a distal direction and aspiration of fluid through the medical valve (110, 111, 210, 211, 310) in a proximal direction; a septum (122, 222, 322) coupled to the housing (120, 220), the septum (122, 222, 322) comprising a proximal surface, a distal surface, and a selectively openable closure (174, 274, 374) that extends through a full thickness of the septum (122, 222, 322) between the proximal surface and the distal surface, wherein the closure (174, 274, 374) is positioned within the chamber; and a plurality of projections (144, 244, 444) that extend away from the sidewall (140, 240, 340), each projection (144, 244, 444) comprising a restriction surface (146, 246) at a distal end thereof that is configured to contact the proximal surface of the septum (122, 222, 322) to oppose movement of a restricted portion of the septum (122, 222, 322) in the proximal direction such that an aspiration cracking pressure required to open the closure (174, 274, 374) to permit fluid flow through the septum (122, 222, 322) in the proximal direction exceeds an infusion cracking pressure required to open the closure (174, 274, 374) to permit fluid flow through the septum (122, 222, 322) in the distal direction, wherein the septum (122, 222, 322) further comprises contact regions at which the septum (122, 222, 322) contacts the restriction surfaces (146, 246) of the plurality of projections (144, 244, 444), the contact regions defining the restricted portion of the septum (122, 222, 322) and having a collective total area that represents only a portion of a total area of the restricted portion of the septum (122, 222, 322).