An Isograft is a graft of tissue between two individuals who are genetically identical (i.e. monozygotic twins). Transplant rejection between two such individuals virtually never occurs.
As monozygotic twins have the same , there is very rarely any rejection of transplanted tissue by the adaptive immune system. Furthermore, there is virtually no incidence of graft-versus-host disease. This forms the basis for why the preferred choice of a physician considering an organ donor will be a monozygotic twin.
In 1993 a research article demonstrated that islet isografts were being transplanted into young diabetic mice [STZ induced diabetic NOD mice] and the mice survived at least about 22 days post transplantation.