(346a) Asymmetric Model Predictive Control Strategies for Blood Glucose Control

Model predictive control (MPC) searches over current and future manipulated inputs to achieve a desired system output. The predictor component forecasts the future system output given a set of input changes that is proposed by the optimizer component. The desired response is iteratively found by minimizing a cost function, also called the control law. The predictive nature, along with an ability to constrain system inputs and outputs, makes MPC an attractive choice for many applications.

In the present study, we explore the use of MPC for blood glucose (BG) control. MPC is a common control strategy found in artificial pancreas (AP) systems used by individuals living with Type 1 diabetes mellitus (T1DM). T1DM is characterized by the loss of insulin production from beta cells in the pancreas, which means insulin must be supplied exogenously by the patient to regulate BG levels. AP systems aim to relieve the burden of T1DM by regulating BG levels with automated insulin injections. Several unique challenges exist for automatic BG control [1]. Briefly, 1) the manipulated input, insulin, provides actuation in one direction: it can only lower BG. 2) There exists an asymmetric risk between hyperglycemia (high BG) and hypoglycemia (low BG). While hyperglycemia should be minimized, hypoglycemia, in the near term, must be avoided entirely.

A MPC strategy used in practice is Loop, a “do-it-yourself” open-source AP system [2]. The predictor component models 4 effects:

• Insulin effect on BG
• Carbohydrate effect on BG
• Retrospective correction, to account for un-modeled BG effects
• Momentum correction, to account for recent BG trends

In this work we examine how the control law currently used in Loop is designed to cope with the challenges of BG control. We then propose a new control law and compare it to the original using the FDA accepted UVA Padova T1DM simulator [3].

Methods

A common control law used in MPC (Equation 1) minimizes the squared predicted residuals of the output (y) from the set-point (r) and squared input changes (∆u) over the prediction (P) and control (M) horizons, respectively. The weight of each contribution is tuned with w.

This control law assumes certainty equivalence, which states that the optimal control action would be the control taken when uncertainty is ignored. However, this assumption does not hold for BG control because of the preference for higher BG levels under uncertainty, per points 1) and 2) above. Thus, this control law is not suitable for BG control.

Loop uses a “coincidence point” type MPC, where the chosen input will force the predicted output to cross a given point at a specified time in the future. Loop delivers insulin in a way that forces the final predicted BG to cross a pre-set value. The amount of insulin required is found from the final predicted BG using a closed form control law (Equation 2). C is a parameter describing the glucose-lowering effect of insulin, which is unique to each patient.

Loop addresses the certainty equivalence violation with two additional heuristic layers: the control and safety overrides. The control override will result in no action being taken if any predicted BG drops below the bottom of a pre-set “correction range,” even if the final predicted BG is above the range. The safety override will cease all insulin delivery if predicted BG ever crosses a lower “suspend threshold”.

We propose a control law that directly addresses the violation of certainty equivalence and considers the entire prediction by controlling to a lower bound (Equation 3).

In words, we find the amount of insulin necessary to force the minimum of the prediction to a lower bound threshold.

To compare the proposed control law to the existing, we pair both control laws to the Loop predictor and simulate across 2-day scenarios consisting of 9 meals using the 11 adult patients contained in the FDA accepted UVA Padova T1DM patient simulator [3]. Performance is evaluated for each scenario with the 70-180 mg/dL time-in-range (TIR) metric [4].

Results

Meals act as a large disturbance to BG control, and Loop relies on the patient to announce the size of the meal and provide a proportional amount of insulin to counteract the meal. Thus, in a first scenario (i) the size of the meal is known, and the correct amount of insulin is provided to counteract the BG-elevating effects of the meal. TIR is found to be similar for both control laws. In reality, the exact meal size is rarely known, so a scenario (ii) is explored where meal size is estimated as 150% of the actual value. This results in the patient providing an excess of insulin at mealtime. The controller with the modified control law maintains a higher TIR with less time in hypoglycemia (BG<70 mg/dL). Full results are provided in Table 1, and average BG traces of the two controllers for this scenario are shown in Figure 1.

The next scenario (iii) explored model inaccuracies. The glucose-lowering effect of insulin assumed by the controller was decreased by 30%. Similar to the previous meal size overestimation scenario, the modified control law increased TIR over the original. The capability of each in a fully closed-loop scenario (iv) was also tested. No meals were announced, requiring the controllers to provide all necessary insulin to regulate BG. Here, the modified control law provided slightly increased TIR.

Conclusion

A new control law for Loop was proposed that directly addresses the violation of certainty equivalence and considers the entire prediction horizon by controlling to a lower bound threshold. TIR was similar for both laws when the exact meal size was known, but the modified control law yielded an improved TIR (95.2% vs 92.0%) with less time in hypoglycemia (4.0% vs 7.5%) when the meal size was overestimated. Additionally, using the modified control law results in slightly improved TIR over the original when model inaccuracies were introduced and in fully closed-loop mode where no meal announcements were provided. In conclusion, MPC is a general framework readily adaptable to applications with unique challenges, such as asymmetric risk and limited control authority, both of which are found in the BG control problem.

[1] Bequette BW. Challenges and recent progress in the development of a closed-loop artificial pancreas. Annu Rev Control. 2012;36(2):255-266.

[2] loopkit.github.io/loopdocs/ [Internet]. LoopDocs; c2019 [cited 2020 Mar 18]. Available from: https://loopkit.github.io/loopdocs/

[3] Dalla Man C, Micheletto F, Lv D, Breton M, Kovatchev BP, Cobelli C. The UVA/PADOVA Type 1 Diabetes Simulator: new features. J Diabetes Sci Technol. 2014;8(1):26-34

[4] Beck RW, Bergenstal RM, Riddlesworth TD, et al. Validation of time in range as an outcome measure for diabetes clinical trials. Diabetes Care. 2019;42:400–6.