(764c) A System Identification and Control Engineering Approach for Designing An Optimized Treatment Plan for Fibromyalgia

There is increasing interest in the medical community towards developing operationalized strategies for treating chronic diseases that take advantage of individual characteristics of the patient for optimizing treatment [1, 2]. In the field of behavioral health, the term "adaptive interventions" has been used to describe individually-tailored strategies for the prevention and treatment of chronic, relapsing disorders [3]. Control systems engineering principles applied to adaptive interventions have been proposed as enablers for more efficacious treatments that minimize waste and enhance intervention potency [4, 5, 6]. This paper will discuss how control engineering principles can be used to design an optimized plan for the treatment of fibromyalgia (FM), a disorder characterized primarily by chronic widespread pain.

The approach is based on a secondary analysis of data collected during a clinical trial using naltrexone, an opioid receptor antagonist, for the treatment of FM [7]. To obtain a dynamical model we apply system identification techniques to extensive daily diary reports completed by intervention participants. These diary reports include self-assessments of outcomes of interest (e.g., general pain symptoms, sleep quality) and additional external variables that affect these outcomes (such as stress, anxiety, and mood). We estimate a multi-input ARX (AutoRegressive with eXogenous inputs) model to best explain the output variance; the procedure is to begin with drug and placebo as inputs, and then systematically include other input variables which contribute to an improvement of the model fit [8].  The ARX model is then simplified to a continuous-time second-order model with zero for each input-output transfer function.  Having obtained a set of dynamical models that describe both manipulated and measured disturbance variables, model predictive control is used as the decision algorithm for automated dosage selection of naltrexone over time. The categorical nature of the dosage assignment, i.e. that fact that the drug dosage levels can only assume discrete values over its domain, creates a need for hybrid model predictive control (HMPC) schemes. In lieu of the conventional tuning approach using objective function weights, a multiple degree-of-freedom formulation is evaluated that enables the user to adjust the speed of setpoint tracking, measured disturbance rejection and unmeasured disturbance rejection independently in the closed loop system [6, 9]. Simulation results for a representative participant in the presence of significant plant-model mismatch and disturbances (both measured and unmeasured) demonstrate the performance and broad-based applicability of a predictive control approach to this class of behavioral intervention problems.

In the final section of the paper, the problem of informative experimental designs that go beyond the traditional approach of applying fixed dosages in a clinical trial is discussed. Flexible dosage designs in literature have been typically related to drug toxicity concerns [10, 11] and do not explicitly target informative data for estimating a dynamical system.  Since the proposed procedure relies on system identification for dynamical modeling, the information content of the input signal and its independence from other signals in the problem are crucial to the success of the overall treatment methodology. Input signals exceeding two levels are required to address nonlinearity, while the experimental protocol must agree with clinical constraints; for example, drug dosage levels must stay within designated settings and should not change abruptly from lowest to highest settings for a given intervention participant.  A new class of optimal input design problems for system identification motivated by this application space that extend the ideas presented in [12] will be presented.

References 

[1] Francis S. Collins. The future of personalized medicine. NIH Medline Plus, 5:2–3, 2010.

[2] Peter Wellstead, Eric Bullinger, Dimitrios Kalamatianos, Oliver Mason, and Mark Verwoerd. The role of control and system theory in systems biology. Annual Reviews in Control, 32(1):33– 47, 2008.

[3] L. M. Collins, S. A. Murphy, and K. L. Bierman. A conceptual framework for adaptive preventive interventions. Prevention Science, 5:185–196, 2004.

[4] D. E. Rivera, M. D. Pew, and L. M. Collins. Using engineering control principles to inform the design of adaptive interventions a conceptual introduction. Drug and Alcohol Dependence, 88(2):S31–S40, 2007.

[5] A. Zafra-Cabeza, D.E. Rivera, L.M. Collins, M.A. Ridao, and E. F. Camacho. A risk-based Model Predictive Control approach to adaptive behavioral interventions in behavioral health, IEEE Transactions in Control Systems Technology, in press, 2011.

[6] Naresh N. Nandola and Daniel E. Rivera. A novel model predictive control formulation for hybrid systems with application to adaptive behavioral interventions. In Proceedings of the 2010 American Control Conference, pages 6286 –6292, June 2010.

[7] Jarred Younger and Sean Mackey. Fibromyalgia symptoms are reduced by low-dose naltrexone: A pilot study. Pain Medicine, 10(4):663–672, 2009.

[8] Sunil Deshpande. A control engineering approach for designing an optimized treatment plan for fibromyalgia. Master’s thesis, Arizona State University, 2011.

[9] W. Wang and D.E. Rivera. Model predictive control for tactical decision-making in semiconductor manufacturing supply chain management. Control Systems Technology, IEEE Transactions on, 16(5):841 –855, Sep. 2008.

[10] Stephen D. Durham, Nancy Flournoy, and William F. Rosenberger. A random walk rule for phase i clinical trials. Biometrics, 53(2):pp. 745–760, 1997.

[11] Lesley M. Arnold, Evelyn V. Hess, James I. Hudson, Jeffrey A. Welge, Sarah E. Berno, and Paul E. Keck. A randomized, placebo-controlled, double-blind, flexible-dose study of fluoxetine in the treatment of women with fibromyalgia. The American Journal of Medicine, 112(3):191 – 197, 2002.

[12] Daniel E. Rivera, Hyunjin Lee, Hans D. Mittelmann, and Martin W. Braun. Constrained multisine input signals for plant-friendly identification of chemical process systems. Journal of Process Control, 19(4):623 – 635, 2009.