Title:
Modeling rejection immunity.

Abstract:
Transplantation is often the only way to treat a number of diseases leading to organ failure. To overcome rejection towards the transplanted organ (graft), immunosuppression therapies are used, which have considerable side-effects and expose patients to opportunistic infections. The development of a model to complement the physician's experience in specifying therapeutic regimens is therefore desirable. The present work proposes an Ordinary Differential Equations model accounting for immune cell proliferation in response to the sudden entry of graft antigens, through different activation mechanisms. The model considers the effect of a single immunosuppressive medication (e.g. cyclosporine), subject to first-order linear kinetics and acting by modifying, in a saturable concentration-dependent fashion, the proliferation coefficient. The latter has been determined experimentally. All other model parameter values have been set so as to reproduce reported state variable time-courses, and to maintain consistency with one another and with the experimentally derived proliferation coefficient.
The proposed model substantially simplifies the chain of events potentially leading to organ rejection. It is however able to simulate quantitatively the time course of graft-related antigen and competent immunoreactive cell populations, showing the long-term alternative outcomes of rejection, tolerance or tolerance at a reduced functional tissue mass. In particular, the model shows that it may be difficult to attain tolerance at full tissue mass with acceptably low doses of a single immunosuppressant, in accord with clinical experience.
The introduced model is mathematically consistent with known physiology and can reproduce variations in immune status and allograft survival after transplantation. The model can be adapted to represent different therapeutic schemes and may offer useful indications for the optimization of therapy protocols in the transplanted patient.