In his early career, he wrote on xenograft hyperacute rejection and in December 1980 was part of the team that performed the first successful human heart transplant using the then newly discovered immunosuppressant cyclosporine.

In 1981, he was part of Bruce Reitz's team that performed the world's first successful combined heart-lung transplant procedure at Stanford University.

Following that, he continued to make significant contributions to heart-lung transplant procedures, and led programmes in cardiothoracic surgery in both adults and children.

In 1986, he was elected president of the International Society for Heart and Lung Transplantation (ISHLT), whilst he was professor and head of cardiothoracic surgery at the University of Minnesota.

[4][6] The first combined heart-lung transplant was accomplished by Denton Cooley in 1968, in Houston, in a two-year-old girl with severe pulmonary hypertension.

[5] Following 1971's Life Magazine's media coverage of failed early heart transplantations, Jamieson published his first papers on xenograft hyperacute rejection in 1974 and 1975.

[1] In 1979, he described a series of successful transplantations in primates using cyclosporine, a fungal derivative whose immunosuppressive properties were reported by Jean-Francois Borel.

[5] On 9 March 1981, Jamieson was part of the team that achieved the first long-term survival following a combined heart-lung transplant procedure, led by Bruce Reitz[17] and accompanied by John Wallwork and Norman Shumway.

[21] By 1989, Jamieson had transferred his entire surgical team, including Michael Peter Kaye,[22] to the University of California, San Diego.

[27][28] By 2011 there were approximately 30 centers worldwide that offered pulmonary endarterectomy and half of the 4,000 procedures performed were being done by Jamieson's programme directorship at University of California, San Diego (UCSD).

[29][30] During his four decades at UCSD, he made modifications to the procedure of PTE, adapted surgical instruments and proposed a classification of CTEPH.

[5] In 1994, Jamieson led the team that performed the first open heart surgery on an orangutan, Karen, at the San Diego Zoo.