A performance limitation for blood glucose regulation in type 1 diabetes accounting for insulin delivery delays

The usual recommendation made by clinicians to type 1 diabetics is that they should inject insulin when consuming a meal or, preferably, slightly earlier. However, in practice, insulin injection maybe delayed. In this paper we develop a fundamental limit on performance when insulin is delivered at some time other than the preferred time. The paper develops an optimal injection policy which minimizes the maximum blood glucose response whilst ensuring that the minimum response does not fall below a pre-specified level. The result provides a “gold standard” against which other insulin injection policies can be compared. Implementation issues are also briefly described.

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