Continuous glucose monitors can measure interstitial glucose concentration in real-time for closed-loop glucose control systems, known as artificial pancreas. These control systems use an insulin feedback to maintain plasma glucose concentration within a narrow and safe range, and thus to avoid health complications. As it is not possible to measure plasma insulin concentration in real-time, insulin models have been used in literature to estimate them. Nevertheless, the significant inter-and intra-patient variability of insulin absorption jeopardizes the accuracy of these estimations. In order to reduce these limitations, our objective is to perform a real-time estimation of plasma insulin concentration from continuous glucose monitoring. Hovorka's glucose-insulin model has been incorporated in an Extended Kalman Filter in which different selected time-variant model parameters have been considered as extended states. The observability of the original Hovorka's model and of several extended models has been evaluated by their Lie derivatives. We have evaluated this methodology with an in-silico study with 100 patients with Type 1 diabetes during 25 hours. Furthermore, it has been also validated using clinical data from 12 insulin pump patients with Type 1 diabetes who underwent four mixed meal studies. Real-time insulin estimations have been compared to plasma insulin measurements to assess performance showing the validity of the methodology here used in comparison with that formerly used for insulin models. Hence, real-time estimations for plasma insulin concentration based on subcutaneous glucose monitoring can be beneficial for increasing the efficiency of control algorithms for the artificial pancreas.
Insulin therapy in type 1 diabetes aims to mimic the pattern of endogenous insulin secretion found in healthy subjects. Glucose-insulin models are widely used in the development of new predictive control strategies in order to maintain the plasma glucose concentration within a narrow range, avoiding the risks of high or low levels of glucose in the blood. However, due to the high variability of this biological process, the exact values of the model parameters are unknown, but they can be bounded by intervals. In this work, the computation of tight glucose concentration bounds under parametric uncertainty for the development of robust prediction tools is addressed.A monotonicity analysis of the model states and parameters is performed. An analysis of critical points, state transformations and application of differential inequalities are proposed to deal with non-monotone parameters. In contrast to current methods, the guaranteed simulations for the glucose-insulin model are carried out by considering uncertainty in all the parameters and initial conditions. Furthermore, no time-discretisation is required, which helps to reduce the computational time significantly. As a result, we are able to compute a tight glucose envelope that bounds all the possible patient's glycemic responses with low computational effort.
Let A = (a ij ) ∈ R n×m be a totally nonpositive matrix with rank(A) = r ≤ min{n, m} and a 11 = 0. In this paper we obtain a characterization in terms of the full rank factorization in quasi-LDU form, that is, A =LDU wherẽ L ∈ R n×r is a block lower echelon matrix, U ∈ R r×m is a unit upper echelon totally positive matrix and D ∈ R r×r is a diagonal matrix, with rank(L) = rank(U ) = rank(D) = r. We use this quasi-LDU decomposition to construct the quasi-bidiagonal factorization of A. Moreover, some properties about these matrices are studied.
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