As a result of serious injury or disease, patients admitted to critical care units often present with elevated blood glucose levels, a condition commonly referred to as stress hyperglycemia1,2,3. It has been shown3 that a reduction in hyperglycemia through the use of intensive insulin administration to achieve tight glucose control (80-130 mg/dL) may have the potential to significantly reduce morbidity and mortality. However, special care must be taken to avoid hypogylcemia, as even a single hypoglycemic event has the capacity to eliminate any benefit of targeted glucose control (TGC)4,5. The careful balance between hyperglycemia reduction and hypoglycemia prevention that must be struck in a clinical setting requires careful and frequent measurement of blood glucose levels at a rate that quickly becomes burdensome on clinical staff and is untenable in a long-term, large-scale deployment.
Commercially available continuous glucose monitors (CGMs) can provide high-frequency measurements of glucose levels allowing for automated insulin and glucose delivery via a model-based control scheme, thereby alleviating the clinical burden associated with TGC. Furthermore, model-based methods can address issues of inter- and intra-patient variability using state and parameter estimation to provide superior blood glucose management and improved patient outcomes. Presented here is the development of error models for testing a proposed control algorithm6 acting on virtual patients with simulated sensors exhibiting noise characteristics statistically similar to those observed in critical care CGM use. Additionally, the formulation of a system of alarms and fail-safes designed to assess sensor and controller performance and tighten or loosen controller constraints according to a rule-based scheme is detailed and evaluated.
We conducted an IRB-approved observational study at the University of Pittsburgh Medical Center (UPMC) where data was collected in duplicate via two subcutaneous Dexcom ®; G4 PLATINUMTM continuous glucose monitors in a cohort of 24 patients during their stay in the intensive care unit. This data provides the basis for the development of CGM error models and the fitting of virtual patients for in silico controller testing.
Simulated sensor error profiles are generated through sampling and integration of changes in CGM error, 
. Stochastic
trajectories of change in error are generated through sampling from representative distributions of 
compiled from the aggregation
of trajectories across all patients. Integration of error derivatives is used here to generate simulated sensor error profiles
as integration provides a source of continuity in the error profile that we believe to be more characteristic of CGM
error and is able to recapitulate drift phenomena that random sampling of absolute errors are unable to accurately
capture.
Patient-specific trajectories of 
are generated by first reconstructing a “true” blood glucose profile from which, the
derivative of error can be calculated. From the CGM data in duplicate, the reconstruction is synthesized as a linear
combination of the CGM signals with variable weights. Weights are regularized to control variance and ensure that the
composite reconstruction approximates a simple mean. Regularization parameters are chosen such that the composite
reconstruction lies within the published error bands of blood glucose measurements taken using a capillary finger-stick glucose
meter.
An alternative method of error reconstruction uses a high-pass filter to extract sensor noise from physiologic changes in glucose.
Physiologic glucose dynamics are slow compared to the sampling period (5 minutes), so high frequency changes in
the CGM signal are likely due to CGM noise and error processes. High frequency components are extracted from
the differenced CGM signal using a high-pass filter and taken as 
, providing a single-sensor alternative to the
reconstruction method. Error profiles using either this high-pass filtering methodology or the previously discussed
reconstruction method will be generated and sampled at points corresponding to the availability of capillary finger-stick
measurements in the collected patient CGM data to evaluate statistical consistency of the proposed models with clinical
observation.
Virtual patients are created by fitting the Intensive Control Insulin-Nutrition-Glucose (ICING) model7, coupled to a subcutaneous insulin model8, to composite reconstructions of blood glucose, constructed using the weighted linear combination of CGM signals discussed above. Virtual patient fitting seeks to minimize sum squared error (SSE) between model predictions and the composite signal using insulin sensitivity (SI) as a bounded time-varying regression parameter. Regularization is used to ensure bounded, smooth and relatively slowly changing SI profiles consistent with physiological response.
Virtual patients are placed under the care of a previously developed6 dual-input (insulin and glucose) zone-control MPC control algorithm, which uses moving horizon estimation (MHE) to provide an estimate of the current state of the controller model. Feedback to the controller is blood glucose as measured in duplicate by two CGMs. In these in silico trials, the simulated blood glucose signal is corrupted by the previously discussed models of sensor error. Using simulated patients and sensor noise, the controller and state estimator are tuned to filter noise and minimize performance loss compared to the unrealistic situation in which CGMs produce perfect measurements.
DSS alarms and fail-safes are developed at multiple points within the proposed control algorithm. At the sensing level, deviations both between individual CGMs and between CGMs and MHE estimated glucose are used to evaluate sensor performance, sensor faults and modify constraints according to a set of rules. A voting system is used to identify the location of single-sensor faults, and faulty measurements are ignored until either the malfunctioning sensor comes back into agreement with the remaining sensor and the estimator or an alarm is sounded. In cases of acceptable CGM-CGM and CGM-estimator consistency, sensor confidence will be assigned a rule-based performance classifier, such as excellent, good or acceptable, based on a critical mean absolute relative deviation over past data of 13% – the maximum error at which the benefits of treating using a continuously available glucose measurement continues to outweigh the potentially detrimental effects of treatment based on an erroneous signal9. Control action will be allowed at the maximum extent of the constraints during conditions of excellent performance and tightened otherwise.
At every time point the estimator a posteriori covariance matrix is updated according to the traditional Kalman update formula and the solution to the discrete algebraic Riccati equation10 and can be used to provide evaluation criteria of estimator performance. If the range of blood glucose is divided into hyper-, hypo- and normoglycemia regimes and a single standard deviation in blood glucose, taken from the covariance matrix, spans multiple regimes, controller constraints are tightened to mitigate unnecessary or dangerous infusions of glucose or insulin potentially resulting in otherwise avoidable hypo- or hyperglycemia. In cases where estimates differ significantly from self-consistent CGM measurements, an alarm to clinicians is raised.
These limitations on control action are proposed to ensure patient safety even in the face of uncertain glucose measurements or
state estimates, as large control actions calculated from an inaccurate state-space pose significant risk to a patient. Care is taken to
choose thresholds, regimes and alarm criteria such that the control algorithm can cope with uncertainty and single-sensor failure, and
only in cases where clinical intervention is expected to be required by the DSS must an alarm be raised. This design is an attempt to
build-in robustness and fault tolerance such that alarms requiring immediate attention are minimized in an effort to
mitigate control fatigue among clinicians. Alarm layers are tested and tuned using virtual patients with modeled CGM
error, as well as unmeasured disturbances such as unannounced meals, edema caused by sensor implantation, and
pressure-induced sensor fluctuation, in order to demonstrate that patient safety can be enhanced through the use of the DSS
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