Abstract
One of the main challenges of glucose control in patients with type 1 diabetes is identifying a control-oriented model that reliably predicts the behavior of glycemia. Here, a review is provided emphasizing the structural identifiability and observability properties, which surprisingly reveals that few of them are globally identifiable and observable at the same time. Thus, a general proposal was developed to encompass four linear models according to suitable assumptions and transformations. After the corresponding structural properties analysis, two minimal model structures are generated, which are globally identifiable and observable. Then, the practical identifiability is analyzed for this application showing that the standard collected data in many cases do not have the necessary quality to ensure a unique solution in the identification process even when a considerable amount of data is collected. The two minimal control-oriented models were identified using a standard identification procedure using data from 30 virtual patients of the UVA/Padova simulator and 77 diabetes care data from adult patients of a diabetes center. The identification was performed in two stages: calibration and validation. In the first stage, the average length was taken as two days (dictated by the practical identifiability). For both structures, the mean absolute error was 16.8 mg/dl and 9.9 mg/dl for virtual patients and 21.6 mg/dl and 21.5 mg/dl for real patients. For the second stage, a one-day validation window was considered long enough for future artificial pancreas applications. The mean absolute error was 23.9 mg/dl and 12.3 mg/dl for virtual patients and 39.2 mg/dl and 36.6 mg/dl for virtual and real patients. These results confirm that linear models can be used as prediction models in model-based control strategies as predictive control.
Highlights
Insulin and glucagon play a key role in glucose homeostasis
Glucagon opposes to the action of insulin, actively stimulating hepatic glycogenolysis and gluconeogenesis and endogenous glucose production (EGP) to enhance a rapid rise in the systemic glucose concentration in postabsorptive and fasting periods, respectively
In [51], the Medtronic Virtual Patient model was presented. This nonlinear model consists of 5 equations that include three-compartment submodels coupled with Bergman’s Minimal model (MM) to describe plasma insulin concentration in response to subcutaneous insulin delivery and insulin effect, and a two-compartment model to describe glucose appearance following a meal based on the maximal model developed by Hovorka et al [52], [53]
Summary
Insulin and glucagon play a key role in glucose homeostasis. Insulin promotes glucose storage as glycogen and inhibits endogenous glucose production (EGP) while promoting glucose utilization in insulin-dependent tissues. In [51], the Medtronic Virtual Patient model was presented This nonlinear model consists of 5 equations that include three-compartment submodels coupled with Bergman’s MM to describe plasma insulin concentration in response to subcutaneous insulin delivery and insulin effect, and a two-compartment model to describe glucose appearance following a meal based on the maximal model developed by Hovorka et al [52], [53]. It is a mathematical model formulated to simulate virtual patients’ glucose dynamics derived from the information provided by the Medtronic MiniMed CareLink sensor-augmented pump during 19 simulation days This linear model consists of three two-compartment submodels for glucose, insulin, and CHO dynamics, yielding a model of 6 states and 9 parameters.
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