Handling Parameter Variations during the Treatment of Type 1 Diabetes Mellitus: In Silico Results

Abstract

Type 1 diabetic patients need a strict treatment to regulate blood glucose concentration in a target range. Despite the development of different control strategies, the model parameter variations, given by physiological changes, can generate an inaccurate treatment and in consequence hyperglycemia and hypoglycemia episodes. Therefore, it is necessary to use control techniques that compensate such effects and maintain the control goals. Here, the effect of parametric variations is examined by the sensitivity analysis from which the most influential parameters in glycemia dynamics are detected. Based on that, an offset-free MPC strategy for impulsive systems is given for the first time in literature and simulated for type 1 diabetes treatment. This scheme along with the impulsive zone MPC with artificial variables reestablishes the normoglycemia behavior since the parameter variations are adequately rejected. However, only parametric variations up to 50% from their nominal values are well compensated, which suggests that more robust formulations are needed to ensure a greater rejection of physiological variations.

Oncolytic virus therapy benefits from control theory

“…Furthermore, antiretroviral treatments have been analysed as impulsive control strategies in which drug uptakes are impulses to force HIV loads to reach and remain at undetectable levels [ 18 , 24 , 25 ]. An impulsive control approach has also been used in the context of type-1 diabetes to regulate the injection of insulin [ 26 , 27 ]. The results highlight that the impulsive control scheme delivers reasonable treatment regimes in both contexts to achieve therapeutic goals despite parameter and modelling uncertainties [ 24 , 25 , 27 , 28 ].…”

Performance Analysis of Different Embedded Systems and Open-Source Optimization Packages Towards an Impulsive MPC Artificial Pancreas

“…In Table 1 , four impulsive MPC formulations are reported. These have been previously tested in simulation scenarios via MATLAB for T1D treatment ( 11 ). The order in which they are reported in Table 1 is according to their complexity, from the standard formulation to steer the state to a set-point to a more complex formulation that corrects plant-model mismatches and steers the state to an equilibrium target zone.…”

“…From these, MPC has received increasing attention due to its good performance in simulation and clinical tests ( 5 , 6 ). Some MPC works in literature are the zone MPC ( 7 ) which incorporated the glycemia target as a set instead of a single point, some MPC designs with asymmetric cost function ( 8 , 9 ), an MPC which drives glycemia to equilibrium sets and considers impulsive inputs ( 10 ), and an offset-free MPC with impulsive inputs that uses a disturbance model to compensate for a plant-model mismatch ( 11 , 12 ). In addition, adaptive control strategies have been formulated as the MPC with adaptive penalization functions for matrices Q, R ( 13 ) and the impulsive offset-free strategy with adaptive features introduced in ( 14 ) and ( 15 ).…”

Adaptive Impulsive Offset-Free MPC to Handle Parameter Variations for Type 1 Diabetes Treatment

“…In this paper, a novel offset-free MPC strategy with adaptive penalty matrices is developed for T1DM treatment. The main features of the strategy are (i) the consideration of insulin input as an impulse; (ii) the use of the MPC formulation with artificial/intermediary variables to achieve equilibrium sets, which provides an enlarged domain of attraction than the standard MPC, and guarantees feasibility and attractivity for the ICS; (iii) the adoption of the offset-free strategy presented by Villa Tamayo et al to take advantage of the information about the plant–model mismatch without an extra modification of the cost function of the MPC. Regarding this, an analysis of the evolution of the estimated mismatch is performed, characterizing the net effect that parametric variations have over it (variations that induce hypoglycemia or hyperglycemia produce a negative or a positive estimation, respectively); and (iv) an automatic adjustment of the MPC penalty matrices consisting of four predefined control tunings according to the sign of the average estimated mismatch, the predicted BG value, and its rate of change, to alternate between aggressive or conservative control actions when required.…”

“…The performance of the adaptive offset-free strategy is evaluated via in-silico tests on 30 virtual patients (10 children, 10 adolescents, and 10 adults) whose parameters are identified from the UVA/Padova simulator . The effect of parametric variations on the blood glucose response was assessed by a sensitivity analysis, finding that the more influential are the insulin sensitivity, the fractional rate of glucose self-regulation, and the insulin diffusion effectiveness . In addition, the intake of meals is considered as not announced to the control strategy.…”