Anne Katrine Duun-Henriksen

Model-Based Closed-Loop Glucose Control in Type 1 Diabetes: The DiaCon Experience

Background: To improve type 1 diabetes mellitus (T1DM) management, we developed a model predictive control (MPC) algorithm for closed-loop (CL) glucose control based on a linear second-order deterministic-stochastic model. The deterministic part of the model is specified by three patient-specific parameters: Insulin sensitivity factor, insulin action time, and basal insulin infusion rate. The stochastic part is identical for all patients but identified from data from a single patient. Results of the first clinical feasibility test of the algorithm are presented. Methods: We conducted two randomized crossover studies. Study 1 compared CL with open-loop (OL) control. Study 2 compared glucose control after CL initiation in the euglycemic (CL-Eu) and hyperglycemic (CL-Hyper) ranges, respectively. Patients were studied from 22:00–07:00 on two separate nights. Results: Each study included six T1DM patients (hemoglobin A1c 7.2% ± 0.4%). In study 1, hypoglycemic events (plasma glucose < 54 mg/dl) occurred on two OL and one CL nights. Average glucose from 22:00–07:00 was 90 mg/dl [74–146 mg/dl; median (interquartile range)] during OL and 108 mg/dl (101–128 mg/dl) during CL (determined by continuous glucose monitoring). However, median time spent in the range 70–144 mg/dl was 67.9% (3.0–73.3%) during OL and 80.8% (70.5–89.7%) during CL. In study 2, there was one episode of hypoglycemia with plasma glucose <54 mg/dl in a CL-Eu night. Mean glucose from 22:00–07:00 and time spent in the range 70–144 mg/dl were 121 mg/dl (117–133 mg/dl) and 69.0% (30.7–77.9%) in CL-Eu and 149 mg/dl (140–193 mg/dl) and 48.2% (34.9–72.5%) in CL-Hyper, respectively. Conclusions: This study suggests that our novel MPC algorithm can safely and effectively control glucose overnight, also when CL control is initiated during hyperglycemia.

Effects of Everyday Life Events on Glucose, Insulin, and Glucagon Dynamics in Continuous Subcutaneous Insulin Infusion–Treated Type 1 Diabetes: Collection of Clinical Data for Glucose Modeling

BACKGROUND In the development of glucose control algorithms, mathematical models of glucose metabolism are useful for conducting simulation studies and making real-time predictions upon which control calculations can be based. To obtain type 1 diabetes (T1D) data for the modeling of glucose metabolism, we designed and conducted a clinical study. METHODS Patients with insulin pump-treated T1D were recruited to perform everyday life events on two separate days. During the study, patients wore their insulin pumps and, in addition, a continuous glucose monitor and an activity monitor to estimate energy expenditure. The sequence of everyday life events was predetermined and included carbohydrate intake, insulin boluses, and bouts of exercise; the events were introduced, temporally separated, in different orders and in different quantities. Throughout the study day, 10-min plasma glucose measurements were taken, and samples for plasma insulin and glucagon analyses were obtained every 10 min for the first 30 min after an event and subsequently every 30 min. RESULTS We included 12 patients with T1D (75% female, 34.3±9.1 years old [mean±SD], hemoglobin A1c 6.7±0.4%). During the 24 study days we collected information-rich, high-quality data during fast and slow changes in plasma glucose following carbohydrate intake, exercise, and insulin boluses. CONCLUSIONS This study has generated T1D data suitable for glucose modeling, which will be used in the development of glucose control strategies. Furthermore, the study has given new physiologic insight into the metabolic effects of carbohydrate intake, insulin boluses, and exercise in continuous subcutaneous insulin infusion-treated patients with T1D.

Model Identification Using Stochastic Differential Equation Grey-Box Models in Diabetes

Background: The acceptance of virtual preclinical testing of control algorithms is growing and thus also the need for robust and reliable models. Models based on ordinary differential equations (ODEs) can rarely be validated with standard statistical tools. Stochastic differential equations (SDEs) offer the possibility of building models that can be validated statistically and that are capable of predicting not only a realistic trajectory, but also the uncertainty of the prediction. In an SDE, the prediction error is split into two noise terms. This separation ensures that the errors are uncorrelated and provides the possibility to pinpoint model deficiencies. Methods: An identifiable model of the glucoregulatory system in a type 1 diabetes mellitus (T1DM) patient is used as the basis for development of a stochastic-differential-equation-based grey-box model (SDE-GB). The parameters are estimated on clinical data from four T1DM patients. The optimal SDE-GB is determined from likelihood-ratio tests. Finally, parameter tracking is used to track the variation in the “time to peak of meal response” parameter. Results: We found that the transformation of the ODE model into an SDE-GB resulted in a significant improvement in the prediction and uncorrelated errors. Tracking of the “peak time of meal absorption” parameter showed that the absorption rate varied according to meal type. Conclusion: This study shows the potential of using SDE-GBs in diabetes modeling. Improved model predictions were obtained due to the separation of the prediction error. SDE-GBs offer a solid framework for using statistical tools for model validation and model development.

Overnight Control of Blood Glucose in People with Type 1 Diabetes

Abstract In this paper, we develop and test a Model Predictive Controller (MPC) for overnight stabilization of blood glucose in people with type 1 diabetes. The controller uses glucose measurements from a continuous glucose monitor (CGM) and its decisions are implemented by a continuous subcutaneous insulin infusion (CSII) pump. Based on a priori patient information, we propose a systematic method for computation of the model parameters in the MPC. Safety layers improve the controller robustness and reduce the risk of hypoglycemia. The controller is evaluated in silico on a cohort of 100 randomly generated patients with a representative inter-subject variability. This cohort is simulated overnight with realistic variations in the insulin sensitivities and needs. Finally, we provide results for the first tests of this controller in a real clinic.

Psychosocial Factors and Adherence to Continuous Glucose Monitoring in Type 1 Diabetes

Several studies have demonstrated beneficial effects of continuous glucose monitoring (CGM) in patients with type 1 diabetes mellitus (T1DM).1–3 In most of the studies, however, a subgroup of patients uses CGM less than recommended or discontinues use. To facilitate treatment adherence in this patient group, thorough understanding of motives for CGM termination is a prerequisite, but only little is known about mechanisms underlying patient adherence to CGM.4–6 Psychosocial factors may affect CGM use because of the constant efforts required of the user to benefit from CGM. To pursue this hypothesis, we invited 24 adults with T1DM from our clinic to take part in a focus group study. Twenty-five ± four months previously, patients had participated in the multicenter Eurythmics Trial2 and started using sensor-augmented pumps (SAPs) during (intervention group) or immediately after completion of the trial (control group). Sensor-augmented pump costs were covered by the Danish health care system. Sixteen patients agreed to participate in the focus group study (Table 1). Twelve were still using SAPs, while four had chosen to cease CGM and continue insulin pump treatment only. Three focus groups were formed based on self-reported CGM use: two groups of current CGM users (six persons in each) and one group of former CGM users (four persons). “CGM use” was defined as sensor use >60% of the time in the past three months. Table 1 Patient Characteristicsa The most notable observation during the focus group sessions was that personal ambitions for metabolic control clearly differed between former and current CGM users. Patients who had discontinued CGM utilization were aware that they could have better metabolic control using CGM; nevertheless, they chose not to. A former user stated: “I know that the sensor improves my hemoglobin A1c (HbA1c)… Intellectually I know that I should wear it. Why don’t I? Now that’s a good question.” Conversely, none of the current users were willing to stop CGM at the expense of a rise in HbA1c. “I want to live a little longer, and I want to be free of all the late complications, so in that respect I don’t think that I have much to negotiate with,” a current CGM user said. All participants praised the glucose curve on the pump display and the arrows indicating rises and falls, but a major complaint coming from both current and former SAP users was CGM inaccuracy. The expression “false security” was used, and two SAP users stated: “I don’t trust it 100% any longer.” “Neither do I. I use it mostly as a guideline.” Continuous glucose monitoring alarms were also vigorously discussed. In particular, alarms caused by inaccurate sensor readings were considered irrelevant interruptions, but also hypo- and hyperalarms that continued after the blood glucose had been corrected due to the inherent time lag of the sensor. Interestingly, former and current users reported different ways of coping with CGM alarms, and the current users seemed less disturbed by alarms. A SAP user explained: “I mute it. You can still follow [the glucose curve] on the display.” In contrast, a former user said: “These nightly alarms…I think you can turn them off, but I never figured out how.” A third important point was that body image played a crucial role for patients in all groups, and to some, it was the most limiting factor of CGM use. Based on this focus group study, we propose that pre-CGM counseling focusing on patient motivation, alarm coping strategies, and body image may increase CGM adherence.

Tuning of Controller for Type 1 Diabetes Treatment with Stochastic Differential Equations

Abstract People with type 1 diabetes need several insulin injections every day to keep their blood glucose level in the normal range and thereby avoiding the acute and long term complications of diabetes. One of the recent treatments consists of a pump injecting insulin into the subcutaneous layer combined with a continuous glucose monitor (CGM) frequently observing the glucose level. Automatic control of the insulin pump based on CGM observations would ease the burden of constant diabetes treatment and management. We have developed a controller designed to keep the blood glucose level in the normal range by adjusting the size of insulin infusions from the pump based on model predictive control (MPC). A clinical pilot study to test the performance of the MPC controller overnight was performed. The conclusion was that the controller relied too much on the local trend of the blood glucose level which is a problem due to the noise corrupted observations from the CGM. In this paper we present a method to estimate the optimal Kalman gain in the controller based on stochastic differential equation modeling. With this model type we could estimate the process noise and observation noise separately based on data from the first clinical pilot study. In doing so we obtained a more robust control algorithm which is less sensitive to fluctuations in the CGM observations and rely more on the global physiological trend of the blood glucose level. Finally, we present the promising results from the second pilot study testing the improved controller.

Assessment of Model Predictive and Adaptive Glucose Control Strategies for People with Type 1 Diabetes

Abstract This paper addresses overnight blood glucose stabilization in people with type 1 diabetes using a Model Predictive Controller (MPC). We use a control strategy based on an adaptive ARMAX model in which we use a Recursive Extended Least Squares (RELS) method to estimate parameters of the stochastic part. We compare this model structure with an autoregressive integrated moving average with exogenous input (ARIMAX) structure, and with an autoregressive moving average with exogenous input (ARMAX) model, i.e. without an integrator. Additionally, safety layers improve the controller robustness and reduce the risk of hypoglycemia. We test our control strategies on a virtual clinic of 100 randomly generated patients with a representative inter-subject variability. This virtual clinic is based on the Hovorka model. We consider the case where only half of the meal bolus is administered at mealtime, and the case where the insulin sensitivity varies during the night. The simulation results demonstrate that the adaptive control strategy can reduce the risks of hypoglycemia and hyperglycemia during the night.

Subdural to subgaleal EEG signal transmission: The role of distance, leakage and insulating affectors

OBJECTIVE To estimate the area of cortex affecting the extracranial EEG signal. METHODS The coherence between intra- and extracranial EEG channels were evaluated on at least 10 min of spontaneous, awake data from seven patients admitted for epilepsy surgery work up. RESULTS Cortical electrodes showed significant extracranial coherent signals in an area of approximately 150 cm(2) although the field of vision was probably only 31 cm(2) based on spatial averaging of intracranial channels taking into account the influence of the craniotomy and the silastic membrane of intracranial grids. Selecting the best cortical channels, it was possible to increase the coherence values compared to the single intracranial channel with highest coherence. The coherence seemed to increase linearly with an accumulation area up to 31 cm(2), where 50% of the maximal coherence was obtained accumulating from only 2 cm(2) (corresponding to one channel), and 75% when accumulating from 16 cm(2). CONCLUSION The skull is an all frequency spatial averager but dominantly high frequency signal attenuator. SIGNIFICANCE An empirical assessment of the actual area of cerebral sources generating the extracranial EEG provides better opportunities for clinical electroencephalographers to determine the location of origin of particular patterns in the EEG.

Overnight glucose control in people with type 1 diabetes

Abstract This paper presents an individualized model predictive control (MPC) algorithm for overnight blood glucose stabilization in people with type 1 diabetes (T1D). The MPC formulation uses an asymmetric objective function that penalizes low glucose levels more heavily. We compute the model parameters in the MPC in a systematic way based on a priori available patient information. The model used by the MPC algorithm for filtering and prediction is an autoregressive integrated moving average with exogenous input (ARIMAX) model implemented as a linear state space model in innovation form. The control algorithm uses frequent glucose measurements from a continuous glucose monitor (CGM) and its decisions are implemented by a continuous subcutaneous insulin infusion (CSII) pump. We provide guidelines for tuning the control algorithm and computing the Kalman gain in the linear state space model in innovation form. We test the controller on a cohort of 100 randomly generated virtual patients with a representative inter-subject variability. We use the same control algorithm for a feasibility overnight study using 5 real patients. In this study, we compare the performance of this control algorithm with the patients usual pump setting. We discuss the results of the numerical simulations and the in vivo clinical study from a control engineering perspective. The results demonstrate that the proposed control strategy increases the time spent in euglycemia.

Predicting Plasma Glucose From Interstitial Glucose Observations Using Bayesian Methods

Background: One way of constructing a control algorithm for an artificial pancreas is to identify a model capable of predicting plasma glucose (PG) from interstitial glucose (IG) observations. Stochastic differential equations (SDEs) make it possible to account both for the unknown influence of the continuous glucose monitor (CGM) and for unknown physiological influences. Combined with prior knowledge about the measurement devices, this approach can be used to obtain a robust predictive model. Method: A stochastic-differential-equation-based gray box (SDE-GB) model is formulated on the basis of an identifiable physiological model of the glucoregulatory system for type 1 diabetes mellitus (T1DM) patients. A Bayesian method is used to estimate robust parameters from clinical data. The models are then used to predict PG from IG observations from 2 separate study occasions on the same patient. Results: First, all statistically significant diffusion terms of the model are identified using likelihood ratio tests, yielding inclusion of σ I s c , σ G p , and σ G s c . Second, estimates using maximum likelihood are obtained, but prediction capability is poor. Finally a Bayesian method is implemented. Using this method the identified models are able to predict PG using only IG observations. These predictions are assessed visually. We are also able to validate these estimates on a separate data set from the same patient. Conclusions: This study shows that SDE-GBs and a Bayesian method can be used to identify a reliable model for prediction of PG using IG observations obtained with a CGM. The model could eventually be used in an artificial pancreas.