453130 Optimal Design of Feasible Clinical Tests for the Identification of Physiological Models of Type 1 Diabetes Mellitus
Type 1 diabetes mellitus (T1DM) is a metabolic disorder characterised by inadequate insulin secretion, causing damaging imbalance to the glucoregulatory system. Cutting edge therapies involve the use of a wearable artificial pancreas (WAP), that is a device capable of maintaining physiological glucose concentration through accurate insulin infusions. A WAP consists of three elements: a glucose sensor, an insulin pump and a control algorithm. Customisation of this device to the individual needs may be accomplished provided that a precise identification of the diabetes physiological model  used in the control algorithm is performed . The identification procedure is typically carried out by means of clinical tests, such as the oral glucose tolerance test (OGTT) or the intravenous glucose tolerance test (IVGTT).
Model-based design of experiment (MBDoE) techniques have already been applied to the design of clinical tests for the identification of individual parameters in subjects with T1DM [3,4], however, the feasibility requirements are not always satisfied. Considering the possibility of improving standard clinical tests, this work applies MBDoE techniques to devise a new physiological test, whose pivotal feature is its implementation feasibility. In order to satisfy this condition, a novel approach based on heuristic indices is hereby introduced to assess several aspects that could impact the most on the practical applicability of the designed protocol. Therefore, the overall evaluation of the test is performed considering 5 indices, taking into account the following features: information, invasivity, safety, duration and number of samples.
A constrained MBDoE strategy, applied to the design of a modified OGTT lasting 5h , where sampling times are optimised while controlling insulin infusion and imposing constraints on safety, generates the optimal test shown in Figure 1a. In the MBDoE formulation, the lower bound on glucose concentration is treated as a hard constraint (hypoglycaemic conditions are harmful even in the short period) while the upper bound is treated as a soft constraint (hyperglycaemic conditions can be tolerated for short periods of time). The designed protocol (MOGTT) is easy to implement both in terms of insulin administration and glucose measurement and also guarantees safety conditions throughout the execution. Evaluation of the designed protocol through in silico studies attests its statistically satisfactory parameter estimation capabilities and its high robustness. Beyond its parameter identification performance, the MOGTT complies with the requirements imposed by feasibility. In fact, the effectiveness of this MBDoE approach is proved by a comparison between the OGTT and the MOGTT protocols in terms of the indices introduced (Figure 1b): safety is deeply improved and information obtainable is maximised.
Finally, the significant enhancement of the information index reflects on the MOGTT exhibiting excellent parameter estimation even upon utterly different parametric sets.
Figure 1: Glucose profiles of the MOGTT and OGTT, along with sampling times and insulin infusion profile, horizontal dots represent glucose bounds imposed in the design (a). Indices radar chart comparing MOGTT and OGTT performance (b). References
 Balakrishnan, N. P.; Rangaiah, G. P.; Samavedham, L. Review and analysis of blood glucose (BG) models for type 1 diabetic patients. Ind. Eng. Chem. Res. 2011; 50(21):12041-12066.
 Cobelli, C.; Renard, E.; Kovatchev, B. Artificial pancreas: Past, present, future. Diabetes 2011; 60(11): 2672-2682.
 Galvanin, F.; Barolo, M.; Macchietto, S.; Bezzo, F. Optimal design of clinical tests for the identification of physiological models of type 1 diabetes in the presence of model mismatch. Med. Biol. Eng. Comput. 2011; 49(3): 263-277.
 Galvanin, F.; Barolo, M.; Macchietto, S.; Bezzo, F. Optimal design of clinical tests for the identification of physiological models of type 1 diabetes mellitus. Ind. Eng. Chem. Res. 2009; 48, 1989-2002.
 Man, C. D.; Campioni, M.; Polonsky, K. S.; Basu, R.; Rizza, R.A.; Toffolo, G. et al. Two-hour seven-sample oral glucose tolerance test and meal protocol: Minimal model assessment of β-cell responsivity and insulin sensitivity in nondiabetic individuals. Diabetes 2005; 54(11): 3265-3273.