(371ad) Adaptive Model Predictive Control with Scenario-Based Reference Optimization for Artificial Pancreas Systems

Type 1 diabetes (T1D) is a chronic autoimmune disease characterized by the destruction of insulin-producing beta cells and subsequent insulin deficiency. Since insulin is necessary to regulate blood glucose concentration (BGC) levels, exogenous insulin is needed for people with T1D. The automation of insulin infusion through technologies that close the loop between glucose sensing and insulin infusion pumps, termed the artificial pancreas (AP) system, is shown to improve glucose control and reduce the likelihood of developing diabetes related complications [1-2]. Despite the proven advantages, closed-loop control of BGC using an AP remains challenging because of the substantive requirements for: (i) reliable models to accurately describe the patient-specific time-varying glucose-insulin dynamics; (ii) efficient predictive control algorithms that regulate the BGC in the presence of stochastic and unknown disturbances; and (iii) cognizance of insulin constraints to prevent an overdose and to improve patient safety [3].

One of the major challenges in the development of an AP is the complex, nonlinear, and only approximately known biochemical and physiological kinetics and dynamics of glucose-insulin metabolism. Reliable glucose-insulin models for online use are not available because of the significant inter- and intra-subject variability in physiology, time-varying delays and nonlinear dynamics caused by both the gradual absorption and utilization of insulin. Furthermore, the transients in blood glucose dynamics affect CGM sensor measurements delays, imprecise or missing information on the time and amount of disturbances like carbohydrate (meal) consumption, and the lingering effects of previously administered insulin provide additional challenges in model development [4].

In this work, we discuss new results on representing the meal effects as a two-component unknown disturbance to the glycemic model identified online. This representation enables, with high accuracy and precision, modeling the meal as an additive large-magnitude disturbance with specific properties that are characteristic for each subject. We discuss incorporation of this representation into a scenario-based trajectory-optimization algorithm [5] that uses a high-fidelity model to account for nonlinear dynamics and delays in detecting carbohydrate consumption. Careful formulation of the meal-response scenarios can provide the online controller with reference trajectories that, when tracked, result in a degree of proactive action in compensating for the meal.

This work builds on our innovations such as the plasma insulin concentration (PIC) estimator to quantify the insulin in the bloodstream designed by using the unscented Kalman filtering technique. The PIC estimator is able to capture the variability in the temporal dynamics of patients by estimating some uncertain model parameters that have significant effects on PIC estimates and be personalized by appropriately initializing the time-varying model parameters by using partial least squares regression models [6].

To obtain an accurate and reliable time-varying glycemic model, we had also extended the optimized version of the recursive predictor-based subspace identification method [7] to better handle unknown disturbances, measurement noise, and variable delays. This is done by incorporation of constraints on the fidelity and accuracy of the identified models, including correctness of the sign of the input-to-output gains and the integration of heuristics to ensure stability of the recursively identified models [8].

We apply the proposed adaptive model predictive control algorithm, which uses recursive subspace identification for tracking the optimal reference trajectories, to the problem of regulating BGC in people with T1D by means of controlled insulin delivery with AP systems. Results obtained with a simulation platform for T1D demonstrate a significant improvement in the AP system, as well as the potential of the approach for use in developing a fully automated AP that can function without any manually-entered information and accommodate major disturbances to the BGC.

References

[1] Cinar, A., Turksoy, K. and Hajizadeh, I., Illinois Inst of Technology, 2016. Multivariable artificial pancreas method and system. U.S. Patent Application 15/171,355.

[2] Maahs, D.M., Buckingham, B.A., Castle, J.R., Cinar, A., Damiano, E.R., Dassau, E., DeVries, J.H., Doyle, F.J., Griffen, S.C., Haidar, A. and Heinemann, L., 2016. Outcome measures for artificial pancreas clinical trials: a consensus report. Diabetes Care, 39(7), pp.1175-1179.

[3] Hajizadeh, I., Rashid, M., and Cinar, A., 2019. Plasma Insulin Cognizant Predictive Control for Artificial Pancreas. Journal of Process Control, 77, pp. 97 - 113.

[4] Cinar, A. and Turksoy, K., 2018. Advances in Artificial Pancreas Systems: Adaptive and Multivariable Predictive Control. Springer.

[5] Paulson, J.A., Heirung, T.A.N., and Mesbah, A., 2019. Fault-tolerant tube-based robust nonlinear model predictive control. In American Control Conference (In Press), Philadelphia, PA.

[6] Hajizadeh, I., Rashid, M., Turksoy, K., Samadi, S., Feng, J., Frantz, N., Sevil, M., Cengiz, E. and Cinar, A., 2017. Plasma insulin estimation in people with type 1 diabetes mellitus. Industrial & Engineering Chemistry Research, 56(35), pp.9846-9857.

[7] Houtzager, I., van Wingerden, J.W. and Verhaegen, M., 2012. Recursive predictor-based subspace identification with application to the real-time closed-loop tracking of flutter. IEEE Transactions on Control Systems Technology, 20(4), pp.934-949.

[8] Hajizadeh, I., Rashid, M., Turksoy, K., Samadi, S., Feng, J., Sevil, M., Hobbs, N., Lazaro, C., Maloney, Z., Littlejohn, E. and Cinar, A., 2018. Incorporating Unannounced Meals and Exercise in Adaptive Learning of Personalized Models for Multivariable Artificial Pancreas Systems. Journal of diabetes science and technology, 12(5), pp.953-966.