Apparatus for use with a delivery catheter comprising: a blood pump comprising: an impeller configured to pump blood through a subject's body; a frame disposed around the impeller, the impeller and frame defining non-radially-constrained configurations in which the impeller is configured to pump blood within the subject's body, and defining radially-constrained configurations in which the impeller and frame are inserted and removed from the subject's body using the delivery catheter, the frame defining struts having a structure that is such that as the frame transitions from a proximal end of the frame toward a center of the frame, the struts pass through junctions, at which pairs of struts branch from a single strut, in a Y -shape; the structure of the struts of the frame being configured such that, in response to a distal end of the delivery catheter and the frame being moved into overlapping positions with respect to each other, the frame is configured to assume its radially-constrained configuration by the frame becoming axially elongated, and is configured to cause the impeller to assume its radially constrained configuration by causing the impeller to become axially elongated, wherein in its radially-non-constrained configuration, the frame defines a proximal conical portion, a distal conical portion, and a cylindrical portion between the proximal conical portion and the distal conical portion, wherein a density of the struts increases from the proximal conical portion to the cylindrical portion, and from the distal conical portion to the cylindrical portion, characterized in that, during operation of the blood pump, the impeller is configured to move with respect to the frame, and a range of movement of the impeller is such that at least a portion of the impeller is disposed within the proximal conical portion of the frame during at least some of the operation of the blood pump, and at least a portion of the impeller is disposed within the cylindrical portion of the frame during at least some of the operation of the blood pump. an impeller configured to pump blood through a subject's body; a frame disposed around the impeller, the impeller and frame defining non-radially-constrained configurations in which the impeller is configured to pump blood within the subject's body, and defining radially-constrained configurations in which the impeller and frame are inserted and removed from the subject's body using the delivery catheter, the frame defining struts having a structure that is such that as the frame transitions from a proximal end of the frame toward a center of the frame, the struts pass through junctions, at which pairs of struts branch from a single strut, in a Y -shape; the structure of the struts of the frame being configured such that, in response to a distal end of the delivery catheter and the frame being moved into overlapping positions with respect to each other, the frame is configured to assume its radially-constrained configuration by the frame becoming axially elongated, and is configured to cause the impeller to assume its radially constrained configuration by causing the impeller to become axially elongated, wherein in its radially-non-constrained configuration, the frame defines a proximal conical portion, a distal conical portion, and a cylindrical portion between the proximal conical portion and the distal conical portion, wherein a density of the struts increases from the proximal conical portion to the cylindrical portion, and from the distal conical portion to the cylindrical portion, characterized in that, during operation of the blood pump, the impeller is configured to move with respect to the frame, and a range of movement of the impeller is such that at least a portion of the impeller is disposed within the proximal conical portion of the frame during at least some of the operation of the blood pump, and at least a portion of the impeller is disposed within the cylindrical portion of the frame during at least some of the operation of the blood pump.