Neural identification of Type 1 Diabetes Mellitus for care and forecasting of risk events

Highlights

• With RHOON we perform identification of the dynamics of blood glucose.

• 35 min of blood glucose were predicted with RHONN.

• Training for the identification and prediction network was done online.

• RHONN predictions are compared with three methods.

Abstract

Glucose–insulin models, testing glucose sensors and support systems for health care decisions play an important role in synthesis of glucose control algorithms. In this work we propose an online glucose–insulin identification using the Recurrent High Order Neural Network (RHONN). Then, the model obtained is used to predict $n$-steps forward of glucose levels, also by RHONN. The used data for identification is from a Type 1 Diabetes Mellitus (T1DM) patient, it was collected from the Continuous Monitoring Glucose System (CMGS) by MiniMed Inc ® and an insulin pump by Paradigm Real-time Insulin Pump ®. RHONN is trained online by Extended Kalman Filter (EKF). The results suggest that it is possible to make a prediction of up to 35 min in the future, which it would help to prevent risky events (hypoglycemia and hyperglycemia). Also shows that, it could be directly connected to a CGMS to help the patient improve the glucose control and even an automatic glucose control algorithm. The proposed Neural Network shows good performance compared to baseline methods in terms of evaluation criteria.

Introduction

Over the past years, Diabetes Mellitus (DM) has become a critical public health problem, being one of the principal causes of death. Just in 2014 it was estimated that approximately 422 million adults were living with diabetes (WHO, 2016). DM is a metabolic disorder whose principal characteristic is that glucose levels increase abnormally to more than 300 mg/dL (hyperglycemia) after food intake (postprandial). It is caused by a deficit in the secretion or a defect in the action of the insulin hormone. This hormone is produced in the pancreas and controls the level of glucose in blood, making it essential for our metabolism. Uncontrolled DM care can lead to complications such as nerve and brain damage, heart diseases, vision loss, amputations, kidney diseases and ultimately death (Dikondwar, 2011, Pranckeviciene et al., 2014).

There are different types of diabetes, one of them is caused by an immunological fault blocking pancreatic insulin production. This is called Type 1 Diabetes Mellitus (T1DM). The conventional treatment of T1DM consists in injections of exogenous insulin to regulate glucose glycemic values. Nevertheless, the regulation is difficult to perform due to disturbances such as meal intake, stress, exercise and the complexity of the glucose (Aathira and Jain, 2014, Tuch et al., 2003). Actually, patients under insulin injections treatment may experience hypoglycemia events, with glucose levels below 70 mg/dL, if the dose is larger than required. Events of hyperglycemia and hypoglycemia where glucose control is deficient are risky if they last for a long time.

A strict glucose control would reduce severe complications linked to the disease. For this reason, the automation of glucose control has been, for a long time, an objective to develop an artificial pancreas. This is, a closed-loop system to automate insulin infusion by means of a continuous glucose monitoring and an insulin pump, see Femat et al. (2009) and Trevitt et al. (2016).

A fundamental requirement for the correct development of control algorithms to connect the insulin pump and glucose monitoring system, is a dynamic model of glucose–insulin Colmegna and Peña (2014). This could be useful, for example, to verify the effectiveness of the controller before clinical trials, that is, to carry out in silico assessments. Therefore, different dynamic models have been reported in the literature to represent the dynamic of glucose–insulin, among them (Hovorka et al., 2002, Man et al., 2014). These reported models are designed through a mass balance to represent organs and tissues that interact in the dynamics of glucose and insulin. The result consists of differential equations that are used in the development of control algorithms. However, in order to develop and validate these types of models, it is necessary to spend a lot of time. This last implies entire knowledge of physical phenomena.

On the other hand, there are other ways of modeling the T1DM dynamics, in which complex medical knowledge is not necessary, only essential knowledge of this disease. These models can be obtained through the stimulus–response method for historical experimental data. We can mention some works of identification of glucose–insulin dynamics, based on linear approximation like the ARX models (AutoRegresive eXternal) (Finan et al., 2008, Van Herpe et al., 2006), ARMA (automatic moving Average) or ARMAX (AutoRegresive Moving Average with eXogenous entries) (Eren-Oruklu et al., 2009). However, linear models are limited; a better way for identification of this kind of dynamics systems are, non-linear identification techniques; such as neural networks (NN) (El-Jabali, 2005), which are a well-established methodology and widely used in engineering problems for applications of modeling and control of non-linear systems. Among the most used structures of neural networks are: feedback and recurrent networks (Alanis et al., 2007, Villaseñor et al., 2018).

The use of NN to model the dynamic of patients with T1DM is not a recent task, actually, it has been considered in different works (El-Baz et al., 2016, El-Jabali, 2005, González-Olvera et al., 2010, Mougiakakou et al., 2006, Sandham et al., 1998, Zarkogianni et al., 2015). The types and architectures of NN used are feedforward (El-Jabali, 2005, Mougiakakou et al., 2006, Sandham et al., 1998, Zarkogianni et al., 2015) also neuro-fuzzy systems (González-Olvera et al., 2010, Zarkogianni et al., 2015). These models developed to represent blood glucose metabolism ruled out the purpose of control; that is, they did not obtain an affine model with NN. In addition, the identified models with NN have been made and reported as one step ahead predictor in engineering problems with satisfactory results (Chang et al., 2007, Villaseñor et al., 2018). However, the information provided by a one step ahead predictor is insufficient and sometimes it is desirable to obtain information several steps in the future.

Multi-step ahead (MSA) prediction consists in knowing future values several steps in the future without any knowledge of the output measurement, which results in a complex task even using NN. MSA is a topic of interest in many scientific studies (Chee and Fernando, 2007, Chen et al., 2013). Some studies have successfully used MSA prediction with NN (Chi and Kim, 2017, Su et al., 1992). For T1DM treatment it is certainly very beneficial to know future glucose conditions, through MSA prediction provided by the models. Incorporating an alarm in the CMGS in real time when the glucose was elevated above the threshold of hyperglycemia or falls below the threshold of hypoglycemia would significantly improve for T1DM therapy (Kamath et al., 2010, McGarraugh, 2010). However, it is desirable to prevent hypoglycemic and hyperglycemic events before they occur (Bremer and Gough, 1999, Eren-Oruklu et al., 2012). An alert generated 20–30 min before a risk event occurs could provide sufficient information for diabetes care (Zecchin et al., 2012). Because of that, a methodology able to prevent future glucose concentration behaviors is necessary (Zecchin et al., 2012). Also, this knowledge of future glucose concentration for a short or long period of time could help a control algorithm supply more insulin to prevent hyperglycemia conditions or to provide less insulin to avoid hypoglycemic conditions.

Actually, some sensors use simple methods to generate an alert when the actual glucose concentration trend is altered and the sensor considers that a threshold will be crossed. Among others, those methods based on a polynomial (Sparacino et al., 2006), AR/ARMA (Gani et al., 2008), state space (Palerm et al., 2005), autoregressive (AR), autoregressive exogenous input (ARX), and autoregressive moving average exogenous input (ARMAX) (Finan et al., 2008), NN models (Pappada et al., 2011, Pérez-Gandía et al., 2010). In the same manner, they are proposed for a short-time glucose prediction (Bequette, 2010, Sparacino et al., 2010), weighted recursive least squares that is used for on-line identification (Eren-Oruklu et al., 2012). In T1DM, a prediction horizon of 30–45 min is sufficient, according to published results.

However, this task is difficult to develop because it is not possible to determine the closely related input information to readjust the performance of the model since they cannot be obtained in time. In addition to this, a small one-step prediction error is accumulated and spread into the future. Because of that most of the NN predictor works implement a training off-line and discard obtain an affine model.

This work is focused in the idea to obtain a non-linear model of glucose level dynamic in consequence of carbohydrate intake and insulin infusion for a T1DM patient, then use the model to make $n$-steps prediction. A good identification approximation could improve the development of a predictor in $n$-steps forward. The proposed model is based on RHONN. The objective is a model that captures the non-linear behavior of the blood glucose in order to design, as future work, an automatic control algorithm that delivers insulin. Also, the obtained model is used for forecasting glucose levels for a short term.

The contributions of this paper are: (1) a neural identifier based on a RHONN, trained on-line with an EKF-based algorithm; (2) the design of an affine model for control purposes; (3) the use of the obtained model as a short term predictor for forecasting the risk events before they occur (hyperglycemia and hypoglycemia). This paper is organized as follows: first, the RHONN, the structure of the $n$-step prediction and the respective training algorithm are shown, followed by the description of the system; experimental results are shown including a comparison with other models used for identification, and finally conclusions are included.