(383c) Multivariable Adaptive Subspace Identification of Blood Glucose Concentration Dynamics for People with Type 1 Diabetes Mellitus

The Artificial Pancreas (AP) system is one of the efficient therapeutic methods for people with type 1 diabetes mellitus (T1DM). This automated system is designed to regulate the blood glucose concentration by using a continuous glucose monitor (CGM), a control system, and an insulin pump [1]. The ultimate goal of an AP system is to simplify the treatment for people with T1DM and reduce the risks associated with hypoglycemia or hyperglycemia. AP research has produced successful results in clinical and outpatient studies, but there are still many limitations that must be addressed. These limitations include exclusive use of glucose information and lack of accurate personalized models to describe the glucose-insulin dynamics in the body over time for use in AP control laws.

One of the challenges to achieve a fully automated and reliable AP is the lack of an accurate model to represent the dynamic changes in the patient’s physiology under various conditions such as exercise and meals. The individualization of the insulin-glucose model is needed because each person has a unique glucose-insulin dynamic behavior. Also, the glucose-insulin dynamics and insulin sensitivity of a person can change from day to day. Moreover, daily activities such as eating and doing physical activities cause large variations in glucose concentration excursions that may not be described accurately by a generalized model. Hence, models with generalized parameters cannot reflect the dynamic behavior of the specific patient in different situations and adaptive personalized glucose-insulin models are necessary for the AP systems.

Subspace model identification (SMI) methods are effective data-driven techniques for identifying state-space models from multi-input and multi-output (MIMO) measurements of a dynamic system. These methods build structured block Hankel matrices using input and output data to retrieve certain subspaces that are related to the system matrices. In this work, a novel closed-loop/open-loop recursive SMI algorithm based on the optimized version of the Predictor-Based Subspace Identification (PBSID) method, the so-called PBSIDopt method is used to identify the glucose–insulin model [2, 3]. Since the techniques for data-based modeling utilize input and output data to identify a model, for a number of cases, although the working system is inherently stable, some samples with high noise levels or unknown disturbances may cause the identified model to be unstable. So, different steps have been suggested to guarantee the stability of the identified system.

The proposed method is able to provide a stable time-varying individualized state space model with glucose concentration values as output (from a CGM sensor) based on estimation of plasma insulin concentration and meal absorption rate (from an Unscented Kalman filter based on Hovorka’s glucose-insulin dynamic model) and biometric variables (Metabolic Equivalent of Task values reported by BodyMedia SenseWear sports armband) as inputs [4, 5, 6]. Adaptive identification (every 5 minutes) allows the model to be valid over various daily life conditions without providing meal and exercise information.

Model identification and validation are based on clinical data from closed-loop experiments. The models are evaluated by means of various performances indices: Variance accounted for (VAF), Root mean square error (RMSE), Normalized root mean square error (NRMSE), Mean square error (MSE) and Normalized mean square error (NMSE). The proposed method provides a stable personalized time-varying state space model over time. The approach proposed in this work has shown a strong potential to identify a consistent glucose–insulin model in real time for use in an AP system.

References

[1] Cinar, A.; Turksoy, K.; Hajizadeh, I. Multivariable artificial pancreas method and system. 2016; US Patent App. 15/171, 355.

[2] Houtzager, I.; van Wingerden, J.-W.; Verhaegen, M. Fast-array recursive closed-loop subspace model identification. IFAC Proceedings Volumes, 2009, 42 (10), 96-101.

[3] Hajizadeh, I.; Rashid, M.; Turksoy, K.; Samadi, S.; Feng, J.; Sevil, S.; Frantz, N.; Lazaro, C.; Maloney, Z.; Littlejohn, E.; Cinar, A. Multivariable Recursive Subspace Identification with Application to Artificial Pancreas Systems. IFAC-Papers Online. 2017, Accepted.

[4] Hajizadeh, I.; Turksoy, K.; Cengiz, E.; Cinar, A. The extended and unscented Kalman filtering methods for real-time plasma insulin concentration estimation in an artificial pancreas control system for patients with type 1 diabetes. Annual Meeting AIChE. 2016.

[5] Hajizadeh, I.; Turksoy, K.; Cengiz, E.; Cinar, A. Real-time estimation of plasma insulin concentration using continuous subcutaneous glucose measurements in people with type 1 diabetes. Proceedings of the American Control Conference (ACC). Seattle, WA, 2017.

[6] Hovorka, R.; Canonico, V.; Chassin, L. J.; Haueter, U.; Massi-Benedetti, M.; Federici, M. O.; Pieber, T. R.; Schaller, H. C.; Schaupp, L.; Vering, T.; Wilinska, M. E. Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes. Physiol. Meas. 2004, 25, 905.