Use of Kalman Filtering in State and Parameter Estimation of Diabetes Models

Diabetes continues to affect many lives every year, putting those affected by it at higher risk of serious health issues. Despite many efforts, there currently is no cure for diabetes. Nevertheless, researchers continue to study diabetes in hopes of understanding the disease and how it affects people, creating mathematical models to simulate the onset and progression of diabetes. Recent research by David J. Albers, Matthew E. Levine, Andrew Stuart, Lena Mamykina, Bruce Gluckman, and George Hripcsak1 has suggested that these models can be furthered through the use of Data Assimilation, a regression method that synchronizes a model with a particular set of data by estimating the system\u27s states and parameters. In my thesis, I explore how Data Assimilation, specifically different types of Kalman filters, can be applied to various models, including a diabetes model. 1Albers, David J, Matthew E Levine, Andrew Stuart, Lena Mamykina, Bruce Gluckman, and George Hripcsak. 2018. Mechanistic machine learning: how data assimilation leverages physiologic knowledge using bayesian inference to forecast the future, infer the present, and phenotype. JAMIA 25(10):1392–1401. doi:10.1093/jamia/ocy106. https: //doi.org/10.1371/journal.pone.0048058

State Estimation of Glucose and Insulin Dynamics

Process simulation and state estimation have very important applications in chemical engineering as well as the biomedical field. Diabetes is a rapidly growing disease in the United States with 29 million people already diagnosed. The estimation of glucose and insulin concentration in patients is necessary in order to effectively treat diabetes. The Bergman Minimal Model is a popular process model that is used to simulate glucose and insulin dynamics. A simulation of this model was created based on estimated parameters for the model from historical data. This thesis investigated the estimation of glucose concentration, insulin concentration, and effect of active insulin using the extended Kalman filter, unscented Kalman filter, ensemble Kalman filter, and sequential Monte Carlo Particle filter. The performance of the filters was compared using root mean squared error. The filters were studied for the cases of good filter initialization, poor filter initialization, plant-model mismatch, increased measurement noise, and multiple glucose ingestions

State Estimation of Glucose and Insulin Dynamics

Process simulation and state estimation have very important applications in chemical engineering as well as the biomedical field. Diabetes is a rapidly growing disease in the United States with 29 million people already diagnosed. The estimation of glucose and insulin concentration in patients is necessary in order to effectively treat diabetes. The Bergman Minimal Model is a popular process model that is used to simulate glucose and insulin dynamics. A simulation of this model was created based on estimated parameters for the model from historical data. This thesis investigated the estimation of glucose concentration, insulin concentration, and effect of active insulin using the extended Kalman filter, unscented Kalman filter, ensemble Kalman filter, and sequential Monte Carlo Particle filter. The performance of the filters was compared using root mean squared error. The filters were studied for the cases of good filter initialization, poor filter initialization, plant-model mismatch, increased measurement noise, and multiple glucose ingestions

State Estimation of Glucose and Insulin Dynamics

Process simulation and state estimation have very important applications in chemical engineering as well as the biomedical field. Diabetes is a rapidly growing disease in the United States with 29 million people already diagnosed. The estimation of glucose and insulin concentration in patients is necessary in order to effectively treat diabetes. The Bergman Minimal Model is a popular process model that is used to simulate glucose and insulin dynamics. A simulation of this model was created based on estimated parameters for the model from historical data. This thesis investigated the estimation of glucose concentration, insulin concentration, and effect of active insulin using the extended Kalman filter, unscented Kalman filter, ensemble Kalman filter, and sequential Monte Carlo Particle filter. The performance of the filters was compared using root mean squared error. The filters were studied for the cases of good filter initialization, poor filter initialization, plant-model mismatch, increased measurement noise, and multiple glucose ingestions

Mechanistic machine learning: how data assimilation leverages physiologic knowledge using Bayesian inference to forecast the future, infer the present, and phenotype

We introduce data assimilation as a computational method that uses machine learning to combine data with human knowledge in the form of mechanistic models in order to forecast future states, to impute missing data from the past by smoothing, and to infer measurable and unmeasurable quantities that represent clinically and scientifically important phenotypes. We demonstrate the advantages it affords in the context of type 2 diabetes by showing how data assimilation can be used to forecast future glucose values, to impute previously missing glucose values, and to infer type 2 diabetes phenotypes. At the heart of data assimilation is the mechanistic model, here an endocrine model. Such models can vary in complexity, contain testable hypotheses about important mechanics that govern the system (eg, nutrition’s effect on glucose), and, as such, constrain the model space, allowing for accurate estimation using very little data

Insulin Estimation and Prediction A REVIEW OF THE ESTIMATION AND PREDICTION OF SUBCUTANEOUS INSULIN PHARMACOKINETICS IN CLOSED-LOOP GLUCOSE CONTROL

This work was supported by the Spanish Ministry of Economy and Competitiveness (MINECO) through grant DPI2013-46982-C2-1-R and the EU through FEDER funds.Bondía Company, J.; Romero Vivó, S.; Ricarte Benedito, B.; Diez, J. (2018). Insulin Estimation and Prediction A REVIEW OF THE ESTIMATION AND PREDICTION OF SUBCUTANEOUS INSULIN PHARMACOKINETICS IN CLOSED-LOOP GLUCOSE CONTROL. IEEE Control Systems. 38(1):47-66. https://doi.org/10.1109/MCS.2017.2766312S476638