A multi-lumen intravenous catheter for use in treating a patient's blood comprising an elongated cylindrical tube with at least first, second and third lumens formed inside. The first lumen is adapted to accept a guide wire for guiding the catheter during insertion into a blood vessel of the patient or therapeutics for introduction into the patient's bloodstream. The second lumen is adapted to return treated blood to the patient's blood vessel and has a smooth, circular or ellipsoidal cross-section. The third lumen is adapted to extract blood from the patient's blood vessel for treatment and has a substantially elliptical or football-shaped cross-section and a cross-sectional area which is 10 to 30 percent larger than a cross-sectional area of the second lumen. Despite such unbalanced cross-sections, the second and third lumens have substantially equal blood flow rates during treatment of the patient's blood. Also, the intake and return flow rates are improved for a given cross-sectional area of the catheter while the hydrostatic pressures within the lumens stay within maximum acceptable hydrostatic pressure limits for the patient.