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

Duun‐Henriksen, Anne Katrine; Schmidt, Signe; Røge, Rikke Meldgaard; Møller, Jan Kloppenborg; Nørgaard, Kirsten; Jørgensen, John Bagterp; Madsen, Henrik

doi:10.1177/193229681300700220

Cited by 55 publications

(41 citation statements)

References 18 publications

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“…In a more realistic clinical setup, the parameter estimation can be done at a lesser frequency, for example once a day, using maximum likelihood estimation or maximum a posteriori estimation. [33][34][35] A previous work showed the feasibility of model identification using CGM data only. 35 The parameter estimation also allows to quantify the degree of uncertainty of the states, σ, which is then used in the CDUKF.…”

Section: Discussionmentioning

confidence: 99%

An Adaptive Nonlinear Basal-Bolus Calculator for Patients With Type 1 Diabetes

Boiroux¹,

Aradóttir²,

Nørgaard

et al. 2016

J Diabetes Sci Technol

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Background: Bolus calculators help patients with type 1 diabetes to mitigate the effect of meals on their blood glucose by administering a large amount of insulin at mealtime. Intraindividual changes in patients physiology and nonlinearity in insulinglucose dynamics pose a challenge to the accuracy of such calculators. Method:We propose a method based on a continuous-discrete unscented Kalman filter to continuously track the postprandial glucose dynamics and the insulin sensitivity. We augment the Medtronic Virtual Patient (MVP) model to simulate noise-corrupted data from a continuous glucose monitor (CGM). The basal rate is determined by calculating the steady state of the model and is adjusted once a day before breakfast. The bolus size is determined by optimizing the postprandial glucose values based on an estimate of the insulin sensitivity and states, as well as the announced meal size. Following meal announcements, the meal compartment and the meal time constant are estimated, otherwise insulin sensitivity is estimated. Results:We compare the performance of a conventional linear bolus calculator with the proposed bolus calculator. The proposed basal-bolus calculator significantly improves the time spent in glucose target (P < .01) compared to the conventional bolus calculator. Conclusion:An adaptive nonlinear basal-bolus calculator can efficiently compensate for physiological changes. Further clinical studies will be needed to validate the results.

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Section: Discussionmentioning

confidence: 99%

An Adaptive Nonlinear Basal-Bolus Calculator for Patients With Type 1 Diabetes

Boiroux¹,

Aradóttir²,

Nørgaard

et al. 2016

J Diabetes Sci Technol

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“…UKF and observers using sigma points in general rely on the assumption that the state variables and disturbances have Gaussian distribution. However, it has been reported [24] that the blood glucose concentration usually follows lognormal distribution instead of the Gaussian distribution. Therefore, we introduced the transformation T , which substitutes selected elements of a vector or matrix with their natural logarithm if they are positive real numbers.…”

Section: A Observermentioning

confidence: 99%

Long-term prediction for T1DM model during state-feedback control

Szalay

Benyó

Kovács

2016

2016 12th IEEE International Conference on Control and Automation (ICCA)

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Abstract-Avoiding low glucose concentration is critically important in type-1 diabetes treatment. Predicting the future plasma glucose levels could ensure the safety of the patient. However, such estimation is no trivial task. The current paper proposes a predictor framework which stems from Unscented Kalman filter and works during closed-loop control, that can predict hazardous glucose levels in advance. Once the blood glucose concentration starts to rise, the predictor activates and estimates future glucose levels up to 3 hours, confirming whether the controller can endanger the patient. The capabilities of the framework is presented through simulations based on the SimEdu validated in-silico simulator.

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“…We augment this model with the CGM noise model developed by Facchinetti et al (2014), and we reformulate this model as a stochastic differential equation-grey box (SDE-GB) model as in Duun-Henriksen et al (2013). A SDE-GB model is a model in the form…”

Section: Physiological Modelmentioning

confidence: 99%

“…They usually consist either of a system of ordinary differential equations (ODEs) (e.g. the models developed by Hovorka et al (2004); Kanderian et al (2009);Dalla Man et al (2014)), or a system of stochastic differential equations (SDEs) (Duun-Henriksen et al (2013)). The former uses in most cases least squares fitting, while the latter uses maximum likelihood for parameter identification.…”

Section: Introductionmentioning

confidence: 99%

Model Identification using Continuous Glucose Monitoring Data for Type 1 Diabetes

et al. 2016

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This paper addresses model identification of continuous-discrete nonlinear models for people with type 1 diabetes using sampled data from a continuous glucose monitor (CGM). We compare five identification techniques: least squares, weighted least squares, Huber regression, maximum likelihood with extended Kalman filter and maximum likelihood with unscented Kalman filter. We perform the identification on a 24-hour simulation of a stochastic differential equation (SDE) version of the Medtronic Virtual Patient (MVP) model including process and output noise. We compare the fits with the actual CGM signal, as well as the short-and long-term predictions for each identified model. The numerical results show that the maximum likelihood-based identification techniques offer the best performance in terms of fitting and prediction. Moreover, they have other advantages compared to ODE-based modeling, such as parameter tracking, population modeling and handling of outliers.

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

Cited by 55 publications

References 18 publications

An Adaptive Nonlinear Basal-Bolus Calculator for Patients With Type 1 Diabetes

An Adaptive Nonlinear Basal-Bolus Calculator for Patients With Type 1 Diabetes

Long-term prediction for T1DM model during state-feedback control

Model Identification using Continuous Glucose Monitoring Data for Type 1 Diabetes

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