Metodo Matematico Para Transplantes

Theoretical Biology and Medical Modelling
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Modeling Rejection Immunity
Theoretical Biology and Medical Modelling 2012, 9:18 doi:10.1186/1742-4682-9-18

Andrea De Gaetano MD,PhD (andrea.degaetano@biomatematica.it) Alice Matone Dr(alice.matone@biomatematica.it) Annamaria Agnes MD (anna_td@hotmail.it) Pasquale Palumbo PhD (pasquale.palumbo@iasi.cnr.it) Francesco Ria MD (fria@rm.unicatt.it) Sabina Magalini MD (sabina.magalini@rm.unicatt.it)

ISSN Article type Submission date Acceptance date Publication date Article URL

1742-4682 Research 18 April 2012 20 May 2012 20 May 2012 http://www.tbiomed.com/content/9/1/18

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© 2012 De Gaetano et al. ; licensee BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

Modeling Rejection Immunity
Andrea De Gaetano1∗ , Alice Matone1 , Annamaria Agnes2 , Pasquale Palumbo1 , Francesco Ria3 and Sabina Magalini2
1 CNR-IASI BioMatLab, UCSC Largo A. Gemelli 8, 00168 Rome, Italy 2 Department of Surgery-Transplantation Service Catholic University, A. Gemelli Hospital, Rome, Italy 3 Institute of General Pathology Catholic University, Largo F. Vito 1, 00168 Rome,Italy

Email: Andrea De Gaetano∗ - andrea.degaetano@biomatematica.it; Alice Matone - alice.matone@biomatematica.it; Annamaria Agnes - anna_td@hotmail.it; Pasquale Palumbo - pasquale.palumbo@iasi.cnr.it; Francesco Ria - fria@rm.unicatt.it; Sabina Magalini - sabina.magalini@rm.unicatt.it;
∗ Corresponding author

Abstract
Background
Transplantation is often the only way to treat a number ofdiseases 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 DifferentialEquations 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 hasbeen 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.

Results
The proposed model substantially simplifies the chain of events potentially leading to organ rejection. It is however able to simulatequantitatively 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....