Apparatus for use in dialyzing a patient comprising a hemodialysis catheter comprising an elongated body having a proximal and a distal end, wherein the distal end terminates in a substantially planar distal end surface; first and second lumens extending from the proximal end to the distal end, wherein the lumens terminate on the distal end surface in first and second mouths, arranged in side-by-side configuration, and further wherein the lumens are separated by a septum; and first and second longitudinal slots formed in the distal end of the elongated body and communicating with the interiors of the lumens, the slots opening on the distal end surface; wherein the slots each have a length and a width, relative to the dimensions of the lumens and the rate of blood flow to be passed through the hemodialysis catheter, so as to minimize undesirable recirculation of dialyzed blood. given lumen is to be used for a suction function, the primary blood flow will enter the proximal end of the longitudinal slot associated with that lumen, whereby to minimize undesirable recirculation of dialyzed blood.