Improving the insulin therapy for diabetic patients using optimal impulsive disturbance rejection: Continuous time approach

Abstract

The paper proposes a new model-based optimization approach to improve the clinical efficiency of compensatory insulin bolus treatment in diabetic patients, aiming to mitigate the consequences of diabetes. The most important contribution of this paper is a novel methodology for determining the optimal parameters of insulin treatment, namely the size and timing of insulin boluses, to effectively compensate for carbohydrate intake. This concept can be seen as the so-called optimal model-based bolus calculator. The presented theoretical framework deals with the problem of optimal disturbance rejection in impulsive systems by minimizing an integral quadratic cost function. The methodology considers a personalized empirical transfer function model with static gains and time constants as the only parameters assumed to be known, making the bolus calculator more straightforward to implement in clinical practice. Contrary to other techniques, the proposed methodology considers impulsive insulin administration in the form of boluses, which is more feasible than continuous infusion. In contrast to the conventional bolus calculator, the proposed algorithm allows for maximizing therapy performance by optimizing the relative time of insulin bolus administration with respect to carbohydrate intake. Another feature to highlight is that the solution of the optimization problem can be obtained analytically, hence no numerical iterative solvers are required. Additionally, the continuous-time domain approach allows for a much finer adjustments of the insulin administration timing compared to discrete-time models. The proposed approach was validated in an in-silico study, which demonstrated the importance of systematically determined insulin–carbohydrate ratio and the relative delay between disturbance and its compensation. The results showed that the proposed optimal bolus calculator outperforms the traditional suboptimal formula.