Denton A. Cooley, the renowned surgeon who was the first to implant a totally artificial heart in a patient and in the process set off one of medicine’s greatest feuds, died on Friday at his home in Houston. He was 96. The Texas Heart Institute, which Dr. Cooley founded, confirmed his death. For more than six decades his name was inextricably linked to that of his mentor and former partner, Dr. Michael E. DeBakey, the developer of the artificial heart. Their pioneering techniques for surgery on the heart and blood vessels have helped tens of thousands of patients. After starting medical school in Galveston, he transferred to Johns Hopkins in Baltimore, earning a medical degree in 1944. Dr. DeBakey and Dr. Cooley devised operations to repair potentially fatal bulges in aortas and to bypass arteriosclerotic damage in neck and leg arteries that could lead to strokes. In 1962, Dr. Cooley founded the Texas Heart Institute at St. Luke’s and became its president. He also taught at the University of Texas and Baylor medical schools in Houston. At his peak, Dr. Cooley was said to be the busiest heart surgeon in the United States, performing many operations a day using an assembly-line approach. Dr. Cooley had homes in Houston and in Galveston, Tex. His wife of 67 years, the Louise Thomas Cooley, died before him, as did a daughter, Florence Talbot Cooley. His survivors include four other daughters, Mary Cooley Craddock, Dr. Susan Cooley, Dr. Louise Cooley Davis and Helen Cooley Fraser; 16 grandchildren; and 17 great-grandchildren.