Feedback control of the immune response of renal transplant recipients with inequality constraints

This paper describes a model of the immunologic response of latent viruses and a donor kidney in a renal transplant recipient. An optimal control problem with state variable inequality constraints is considered to maintain the balance between over-suppression where latent viruses are reactivated and under-suppression where the transplanted kidney is rejected. A feedback methodology based on the model predictive control (MPC) method is proposed to design (sub)optimal treatment regimes. In addition, the problem of implementing the MPC methodology and nonlinear Kalman filter with inaccurate or incomplete observation data and long measurement periods is addressed. The results of numerical simulations show that a (sub)optimal dynamic immunosuppression therapy method can help strike a balance between the over-suppression and under-suppression of the immune system.

[1]  F. Pereyra,et al.  Prevention and treatment of cytomegalovirus infection in solid organ transplant recipients , 2004, Current opinion in infectious diseases.

[2]  F. Daum.  Nonlinear filters: beyond the Kalman filter , 2005, IEEE Aerospace and Electronic Systems Magazine.

[3]  Harvey Thomas Banks,et al.  A state‐dependent Riccati equation‐based estimator approach for HIV feedback control , 2006 .

[4]  B. Adams,et al.  HIV dynamics: Modeling, data analysis, and optimal treatment protocols , 2005 .

[5]  I. Rosenberg,et al.  Serum cystatin C as a determinant of fasting total homocysteine levels in renal transplant recipients with a normal serum creatinine. , 1999, Journal of the American Society of Nephrology : JASN.

[6]  H. Rollag,et al.  Cytomegalovirus infection in renal transplant recipients is associated with impaired survival irrespective of expected mortality risk , 2007, Clinical Transplantation.

[7]  Harvey Thomas Banks,et al.  Feedback control of HIV antiviral therapy with long measurement time , 2011 .

[8]  Guanrong Chen,et al.  Feedback control of a biodynamical model of HIV-1 , 2001, IEEE Transactions on Biomedical Engineering.

[9]  B. Adams,et al.  Dynamic multidrug therapies for hiv: optimal and sti control approaches. , 2004, Mathematical biosciences and engineering : MBE.

[10]  James B. Rawlings,et al.  Tutorial overview of model predictive control , 2000 .

[11]  Harvey Thomas Banks,et al.  Receding Horizon Control of HIV , 2011 .

[12]  A. Levey,et al.  A More Accurate Method To Estimate Glomerular Filtration Rate from Serum Creatinine: A New Prediction Equation , 1999, Annals of Internal Medicine.

[13]  Suzanne Lenhart,et al.  Optimal control of treatments in a two-strain tuberculosis model , 2002 .

[14]  C. Ki,et al.  Real-time PCR assay compared with antigenemia assay for detecting cytomegalovirus infection in kidney transplant recipients. , 2007, Transplantation proceedings.

[15]  Chung Choo Chung,et al.  Optimal Scheduling of Drug Treatment for HIV Infection : Continuous Dose Control and Receding Horizon Control , 2003 .

[16]  S. Joe Qin,et al.  A survey of industrial model predictive control technology , 2003 .

[17]  Kazufumi Ito,et al.  Asymptotic Properties of Receding Horizon Optimal Control Problems , 2002, SIAM J. Control. Optim..

[18]  Ryan Zurakowski,et al.  A model predictive control based scheduling method for HIV therapy. , 2006, Journal of theoretical biology.

[19]  H. T. Banks,et al.  A model for HCMV infection in immunosuppressed patients , 2009, Math. Comput. Model..

[20]  Yanzhao Cao,et al.  Optimal control of vector-borne diseases: Treatment and prevention , 2009 .

[21]  Knut Sydsæter,et al.  Optimal control theory with economic applications , 1987 .

[22]  Lamberto Cesari,et al.  Optimization-Theory And Applications , 1983 .

[23]  J. Watmough,et al.  Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. , 2002, Mathematical biosciences.

[24]  Luc Perrin,et al.  Monitoring of Cytomegalovirus Infection in Solid-Organ Transplant Recipients by an Ultrasensitive Plasma PCR Assay , 2003, Journal of Clinical Microbiology.

[25]  Taesoo Jang,et al.  Modelling and optimal control of immune response of renal transplant recipients , 2012, Journal of biological dynamics.

[26]  Jeehyun Lee,et al.  Free Terminal Time Optimal Control Problem of an HIV Model Based on a Conjugate Gradient Method , 2011, Bulletin of mathematical biology.

[27]  Mohinder S. Grewal,et al.  Kalman Filtering: Theory and Practice Using MATLAB , 2001 .