Professor Muller is recognised as a global authority on kidney and liver transplantation and is a trailblazer in the field of organ transplantation in HIV-positive patients. Currently the head of the University of Cape Town’s (UCT) Division of General Surgery, she initiated a Donation after Cardiac Death programme in 2007 and a transplant programme for HIV-positive patients utilising HIV-positive donors at Groote Schuur Hospital in 2008.

She is a past president of the South African Transplantation Society and incoming president of the international Transplantation Society (TTS). She has been involved in many transplant-related outreach and educational programmes for the public and medical profession.

She has collaborated with many international leaders including professionals from the University of California San Francisco (UCSF), Johns Hopkins University (United States of America) and Lund University (Sweden). Her research influenced the HIV Organ Policy Equity (HOPE) Act in the USA, a law that modified the rules regarding organ donation between HIV-positive individuals.

Her work had been published in the New England Journal of Medicine, Lancet and several other high impact journals.