A discrete segments approach to the optimization of insulin infusion algorithms

• Published in: Computers & mathematics with applications (1987) Vol. 20; no. 4; pp. 207 - 215
• Main Author: Ollerton, R.L.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 1990; Elsevier
• Subjects: Biological and medical sciences; Endocrine pancreas. Apud cells (diseases); Endocrinopathies; Medical sciences; Endocrinopathy; Protein hormone; Pancreatic hormone; Hyperglycemia; Perfusion; Diabetes mellitus; Biomathematics; Mathematical model; Algorithm; Insulin; Optimization
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/0898-1221(90)90328-H

Aim. To derive closed-loop insulin infusion algorithms for the metabolic control of hospitalized, non-insulin-producing subjects. Methodology. Biological systems are frequently complex and non-linear. One hindrance to the application of methods of optimal control theory has been that when they are applied to non-linear systems it is often difficult, if not impossible, to derive a practical closed-loop control algorithm. Because of this, optimal control theory has not produced the same successes in biological areas as in other disciplines. The method of “discrete segments” attempts to avoid the open-loop results of other approaches by considering the control variable to consist of a number of small, discrete sections. With an additional assumption concerning the duration of the “effect” of one of these small sections, the optimization problem presented in this study is reformulated so that individual sections of the control may be found in terms of quantities known at earlier times. The full control strategy is derived by setting partial derivatives of the cost function (with respect to the control segments) equal to zero. The clinical situation of a diabetic patient (normal, insulin resistant or glucose resistant) presenting with mild, post-operative hyperglycaemia (PG = 10 mmol/l) is modelled using the “minimal” model of Bergman et al., as modified for the diabetic state by Furler et al. A cost criterion was postulated and an algorithm for choosing the appropriate infusion rate regime was derived using the “discrete segments” approach. Conclusions. The method of “discrete segments” can be an effective alternative to the usual methods of optimal control theory. The insulin infusion rate algorithm derived in this study has a closed-loop form and procedures good metabolic control in the theoretical framework.