(382e) Control Under Uncertainty in Automated Drug Delivery

Biological processes are complex dynamical systems with significant uncertainties and exogenous disturbances that render their regulation and control a challenging problem. Model predictive control (MPC) formulations, often used in biomedical applications, particularly for controlled drug delivery, are effective in rejecting disturbances and mitigating their effects through receding horizon control. MPC is commonly used in artificial pancreas (AP) systems to automatically compute the required amount of insulin dose to administer in patients living with the chronic disease of type 1 diabetes to regulate their glucose concentrations [1]. Despite recent advancements, the development and commercialization of an AP is challenging because of the complex, nonlinear, and only approximately known biochemical and physiological kinetics and dynamics of glucose–insulin metabolism [2].

High-fidelity predictive models are not readily available for metabolic processes due to the significant variability in human physiology and obscure information on the time and amount of carbohydrate consumption and exercise or physical activity levels. A fully automated AP system eliminating the need for patients to interact with the system and manually enter user inputs for meal and exercise announcements represents a substantial step towards achieving better insulin delivery systems [3]. Recognizing and attenuating the challenging and uncertain disturbances such as meals and exercise that affect the glycemic homeostasis is therefore necessary [4]. Concerning the automation of AP systems, several studies have incorporated unannounced meals through the estimation of time-varying parameters or analysis of glucose trends. Furthermore, additional physiological variables related to physical activity are also considered to automatically accommodate exercise [5]. Despite these efforts, automatically handling of unannounced meals and exercise in adaptive and personalized glycemic models for predictive control in AP systems is not sufficiently studied, while the future progression of the meal and exercise effects is not elucidated because their temporal evolution is uncertain.

Motivated by the above considerations, a stochastic MPC formulation is proposed for handling the uncertain effects of meals and exercise on the future glycemic predictions. The proposed MPC utilizes adaptive models to accurately characterize the time-varying glycemic dynamics. To address the uncertainty in the future projections of the meals and exercise effects, the future evolution of the uncertain variables is modelled using uncertainty sets from which realizations of the uncertain variables are considered in a stochastic control formulation. The optimal insulin infusion rates are then computed with respect to the possible realizations concerning the uncertain variables. The efficacy of the proposed stochastic MPC for handling uncertainty in meals and exercise for glucose control is demonstrated using simulation case studies.

[1] Gondhalekar, R., Dassau, E., and Doyle III, F. J. (2016). Periodic zone-MPC with asymmetric costs for outpatient-ready safety of an artificial pancreas to treat type 1 diabetes. Automatica, 71, 237-246.
[2] Messori, M., Incremona, G. P., Cobelli, C., & Magni, L. (2018). Individualized model predictive control for the artificial pancreas: In silico evaluation of closed-loop glucose control. IEEE Control Syst., 38(1), 86-104.
[3] Turksoy, K., Hajizadeh, I., Samadi, S., Feng, J., Sevil, M., Park, M., Quinn, L., Littlejohn, E., and Cinar, A. (2017). Real-time insulin bolusing for unannounced meals with artificial pancreas. Control Eng. Pract., 59, 159-164.
[4] Bequette, B. W., Cameron, F., Baysal, N., Howsmon, D. P., Buckingham, B. A., Maahs, D. M., and Levy, C. J. (2016). Algorithms for a Single Hormone Closed-Loop Artificial Pancreas: Challenges Pertinent to Chemical Process Operations and Control. Processes, 4(4), 39.
[5] Turksoy, K., Quinn, L., Littlejohn, E., and Cinar, A. (2014). Multivariable adaptive identification and control for artificial pancreas systems. IEEE Trans. Biomed. Eng., 61(3), 883-891.