A heart pump assembly includes an elongate catheter with a proximal portion and a distal portion, a rotor at the distal portion of the elongate catheter, a driveshaft, and a bearing. The rotor can include an impeller blade shaped to induce fluid flow in a first axial direction. The drive shaft may be coupled to or integrally formed with a proximal end of the rotor and can include a pump element formed in a surface of the drive shaft. The bearing can include a bore into which the drive shaft extends. The pump element is shaped so as to induce fluid flow through the bore in a second axial direction which can be the same or opposite to the first axial direction.