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 AM  Vol.8 No.7 , July 2017
An Optimal Control Approach to Structured Treatment Interruptions for HIV Patients: A Personalized Medicine Perspective
Abstract: Highly Active Antiretroviral Therapy (HAART) has changed the course of human immunodeficiency virus (HIV) treatments since its introduction. However, for many patients, long term continuous HAART is expensive and can include problems with drug toxicity and side effects, as well as increased drug resistance. Because of these reasons, some HIV infected patients will voluntarily terminate HAART. Some of these patients will also interrupt the continuous prescribed therapies for short or long periods. After discontinuing HAART, patients will usually experience a rapid increase in viral load coupled with an immediate decline in CD4+ counts. The canonical example of a patient undergoing unsupervised breaks in HAART is that of the “Berlin patient”. In this case, the patient was able to control viral load in the absence of treatment by cycling HAART on and off due to non-related infections. Due to this patient, interest in the use of structured treatment interruptions (STI) as a mechanism to regulate an HIV infection piqued. This paper describes an optimal control approach to determine STI regimen for HIV patients. The optimal STI was implemented in the context of the receding horizon control (RHC) using a mathematical model for the in-vivo dynamics of an HIV type 1 infection. Using available clinical data, we calibrate the model by estimating on a patient specific basis, a best estimable set of parameters using sensitivity analysis and subset selection. We demonstrate how customized STI protocols can be designed through the variation of control parameters on a patient specific basis.
Cite this paper: Attarian, A. and Tran, H. (2017) An Optimal Control Approach to Structured Treatment Interruptions for HIV Patients: A Personalized Medicine Perspective. Applied Mathematics, 8, 934-955. doi: 10.4236/am.2017.87074.
References

[1]   Bell, S.K., Little, S.J. and Rosenberg, E.S. (2010) Clinical Management of Acute HIV Infection: Best Practice Remains Unknown. The Journal of Infectious Diseases, 202, S278-S288.
https://doi.org/10.1086/655655

[2]   Perelson, A.S., Neumann, A.U., Markowitz, M., Leonard, J.M. and Ho, D.D. (1996) HIV-1 Dynamics in Vivo: Virion Clearance Rate, Infected Cell Life-Span, and Viral Generation Time. Science, 271, 1582-1586.
https://doi.org/10.1126/science.271.5255.1582

[3]   Perelson, A.S. and Nelson, P.W. (1999) Mathematical Analysis of HIV-1 Dynamics in Vivo. SIAM Review, 41, 3-44.
https://doi.org/10.1137/S0036144598335107

[4]   Callaway, D. and Perelson, A.S. (2002) HIV-1 Infection and Low Steady State Viral Loads. Bulletin of Mathematical Biology, 64, 29-64.
https://doi.org/10.1006/bulm.2001.0266

[5]   Nelson, P.W., Gilchrist, M.A., Coombs, D., Hyman, J.M. and Perelson, A.S. (2004) An Age-Structured Model of HIV Infection That Allows for Variations in the Production Rate of Viral Particles and the Death Rate of Productively Infected Cells. Mathematical Biosciences and Engineering, 1, 267-288.
https://doi.org/10.3934/mbe.2004.1.267

[6]   Rong, L., Feng, Z. and Perelson, A.S. (2007) Mathematical Analysis of Age-Structured HIV-1 Dynamics with Combination Antiretroviral Therapy. SIAM Journal on Applied Mathematics, 3, 731-756.
https://doi.org/10.1137/060663945

[7]   Brandt, M.E. and Chen, G. (2001) Feedback Control of a Biodynamical Model of HIV-1. IEEE Transactions on Biomedical Engineering, 48, 754-759.
https://doi.org/10.1109/10.930900

[8]   Joshi, H.R. (2002) Optimal Control of an HIV Immunology Model. Optimal Control Applications and Methods, 23, 199-213.
https://doi.org/10.1002/oca.710

[9]   Ge, S.S., Tian, Z. and Lee, T.H. (2005) Nonlinear Control of a Dynamic Model of HIV-1. IEEE Transactions on Biomedical Engineering, 52, 353-361.
https://doi.org/10.1109/TBME.2004.840463

[10]   Adams, B.M., Banks, H.T., Kwon, H.D. and Trani, H.T. (2004) Dynamic Multidrug Therapies for HIV: Optimal and STI Control Approaches. Mathematical Biosciences and Engineering, 2, 223-241.

[11]   David, J.A., Banks, H.T. and Tran, H.T. (2009) HIV Model Analysis under Optimal Control Based Treatment Strategies. International Journal of Pure and Applied Mathematics, 57, 357-392.

[12]   David, J.A., Banks, H.T. and Tran, H.T. (2011) Receding Horizon Control of HIV. Optimal Control Applications and Methods, 32, 681-699.
https://doi.org/10.1002/oca.969

[13]   Banks, H.T., Kwon, H.D., Toivanen, J.A. and Tran, H.T. (2006) A State-Dependent Riccati Equation-Based Estimator Approach for HIV Feedback Control. Optimal Control Applications and Methods, 27, 93-121.
https://doi.org/10.1002/oca.773

[14]   Roy, P.K. and Chatterjee, A.N. (2011) Effect of HAART on CTL Mediated Immune Cells: An Optimal Control Theoretic Approach. In: Sio Long Ao, Ed., Electrical Engineering and Applied Computing, Len Gelman Springer, New York, Vol. 90, 595-607.

[15]   Duwal, S., Winkelmann, S., Schutte, C. and von Kleist, M. (2015) Optimal Treatment Strategies in the Context of “Treatment for Prevention” against HIV-1 in Resource-Poor Setting. PLOS Computational Biology, 11, e1004200.
https://doi.org/10.1371/journal.pcbi.1004200

[16]   Hernandez-Vargas, E.A., Colaneri, P. and Middleton, R.H. (2013) Optimal Therapy Scheduling for a Simplified HIV Infection Model. Automatica, 49, 2874-2880.

[17]   Burth, M., Verghese, G. and Velez-Reyes, M. (1999) Subset Selection for Improved Parameter Estimation in On-Line Identification of a Synchronous Generator. IEEE Transactions on Power Systems, 14, 218-225.
https://doi.org/10.1109/59.744536

[18]   Audoly, S., Bellu, G., D’Angio, L., Saccomani, M.P. and Cobelli, C. (2001) Global Identifiability of Nonlinear Models of Biological Systems. IEEE Transactions on Biomedical Engineering, 48, 55-65.
https://doi.org/10.1109/10.900248

[19]   Xia, X. and Moog, C.H. (2003) Identifiability of Nonlinear Systems with Application to HIV/AIDS Models. IEEE Transactions on Automatic Control, 48, 330-336.
https://doi.org/10.1109/TAC.2002.808494

[20]   Xia, X. (2003) Estimation of HIV/AIDS Parameters. Automatica, 39, 1983-1988.

[21]   Adams, B.M., Banks, H.T., Davidian, M. and Rosenberg, E. (2007) Estimation and Prediction with HIV-Treatment Interruption Data. Bulletin of Mathematical Biology, 69, 563-584.
https://doi.org/10.1007/s11538-006-9140-6

[22]   Lisziewicz, J. and Lori, F. (2002) Structured Treatment Interruptions in HIV/AIDS Therapy. Microbes and Infection, 4, 207-214.

[23]   Lisziewicz, J., Rosenberg, E., Lieberman, J., Jessen, H., Lopalco, L., Siliciano, R., Walker, B. and Lori, F. (1999) Control of HIV Despite the Discontinuation of Antiretroviral Therapy. New England Journal of Medicine, 340, 1683-1683.
https://doi.org/10.1056/NEJM199905273402114

[24]   Lori, F., Lewis, M.G., Xu, J., Varga, G., Zinn, D.E., Crabbs, C., Wagner, W., Greenhouse, J., Silvera, P., Yalley-Ogunro, J., Tinelli, C. and Lisziewicz, J. (2000) Control of SIV Rebound through Structured Treatment Interruptions during Early Infection. Science, 290, 1591-1593.
https://doi.org/10.1126/science.290.5496.1591

[25]   Lori, F. and Lisziewicz, J. (2001) Structured Treatment Interruptions for the Management of HIV Infection. JAMA: The Journal of the American Medical Association, 286, 2981-2987.
https://doi.org/10.1001/jama.286.23.2981

[26]   Adams, B.M. (2005) Non-Parametric Parameter Estimation and Clinical Data Fitting with a Model of HIV Infection. PhD Dissertation, North Carolina State University.

[27]   Banks, H.T., Davidian, M., Hu, S., Kepler, G.M. and Rosenberg, E.S. (2008) Modeling HIV Immune Response and Validation with Clinical Data. Journal of Biological Dynamics, 2, 357-385.
https://doi.org/10.1080/17513750701813184

[28]   Bonhoeffer, S., Rembiszewski, M., Ortiz, G.M. and Nixon, D.F. (2000) Risks and Benefits of Structured Antiretroviral Drug Therapy Interruptions in HIV-1 Infection. AIDS, 14, 2313-2322.
https://doi.org/10.1097/00002030-200010200-00012

[29]   Banks, H.T., Dedui, S. and Ernstberger, S.L. (2007) Sensitivity Functions and Their Uses in Inverse Problems. Journal of Inverse and Ill-Posed Problems, 15, 1-26.
https://doi.org/10.1515/JIIP.2007.001

[30]   Miao, H., Xia, X., Perelson, A.S. and Wu, H. (2011) On Identifiability of Nonlinear ODE Models and Applications in Viral Dynamics. SIAM Review, 53, 3-39.

[31]   Attarian, A.R. (2012) Patient Specific Subset Selection, Estimation and Validation of an HIV-1 Model with Censored Observations under an Optimal Treatment Schedule. PhD Dissertation, North Carolina State University.

[32]   Dempster, A., Laird, N. and Rubin, D. (1977) Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society: Series B, 39, 1-38.

[33]   Banks, H.T. and Tran, H.T. (2009) Mathematical and Experimental Modeling of Physical and Biological Processes. Chapman & Hall/CRC, Boca Raton.

[34]   Finkel, D.E. and Kelley, C.T. (2004) Convergence Analysis of DIRECT Algorithm. OPT Online, 14, 1-10.

[35]   Phillips, A. (2005) Long Term Probability of Detection of HIV-1 Drug Resistance after Starting Antiretroviral Therapy in Routine Clinical Practice. AIDS, 19, 487-494.
https://doi.org/10.1097/01.aids.0000162337.58557.3d

[36]   Paterson, D.L., Swindells, S., Mohr, J., Brester, M., Vergis, E.N., Squier, C., Wagener, M.M. and Singh, N. (2000) Adherence to Protease Inhibitor Therapy and Outcomes in Patients with HIV Infection. Annals of Internal Medicine, 133, 21-30.
https://doi.org/10.7326/0003-4819-133-1-200007040-00004

[37]   Rosenberg, E.S., Davidian, M. and Thomas Banks, H. (2007) Using Mathematical Modeling and Control to Develop Structured Treatment Interruption Strategies for HIV Infection. Drug and Alcool Dependence, 88, S41-S51.

[38]   Bajaria, S.H., Webb, G. and Kirschner, D.E. (2004) Predicting Differential Responses to Structured Treatment Interruptions during HAART. Bulletin of Mathematical Biology, 66, 1093-1118.

[39]   Ortiz, G.M., Wellons, M., Jason, B., Vo, H.T.T., Zinn, R.L., Clarkson, D.E., Loon, K.V., Bonhoeffer, S., Miralles, G.D., Montefiori, D., Bartlett, J.A. and Nixon, D.F. (2001) Structured Antiretroviral Treatment Interruptions in Chronically HIV-1-Infected Subjects. Proceedings of the National Academy of Sciences of the United States of America, 98, 13288-13293.
https://doi.org/10.1073/pnas.221452198

[40]   Garcia, C.E., Prett, D.M. and Morari, M. (1989) Model Predictive Control: Theory and Practice—A Survey. Automatica, 25, 335-348.

[41]   Zurakowski, R. and Teel, A.R. (2006) A Model Predictive Control Based Scheduling Method for HIV Therapy. Journal of Theoretical Biology, 230, 368-382.

[42]   Camacho, E.F. and Bordons, C. (2004) Model Predictive Control Advanced Textbook in Control and Signal Processing. Springer, Berlin.

 
 
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