Modeling glycemia in humans by means of Grammatical Evolution
Graphical abstract
Introduction
Diabetes mellitus is a disease caused by a defect in either the secretion or in the action of insulin, which is essential for the control of blood glucose levels. Both of them cause in cells not to assimilate the sugar and, as a consequence, there is a rise in blood glucose levels, or hyperglycemia. Several types of diabetes differ in origin. According to the ADA (American Diabetes Association) we can distinguish four types of diabetes:
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Type 1 Diabetes (T1DM): cells do not produce insulin because of an autoimmune process. Currently, requires the person to inject insulin or wear an insulin pump.
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Type 2 Diabetes (T2DM): results from insulin resistance, where cells fail to use insulin properly, sometimes combined with an absolute insulin deficiency.
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Gestational diabetes: appears in the gestation period in one out of ten pregnant women. Pregnancy is a change in the body's metabolism, since the fetus uses the mother's energy for food, oxygen and others. This causes a decrease in the secretion of insulin from the mother.
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Other types: such as problems on β-cells, genetic defects affecting insulin action, induced by drugs, and genetic syndromes.
In most cases, diabetic patients with long time evolution need exogenous insulin either injected into various injection doses, or introduced by an insulin pump. It is important to maintain good glycemic control to prevent not only from the acute complications specific to diabetes (diabetic ketoacidosis and hypoglycemia, defined as blood glucose value less than 70 mg/dl), but also from a set of multi-chronic complications associated with diabetic patients: nephropathy, retinopathy, microangiopathy and macroangiopathy.
In recent years, it has been shown that a strict glycemic control in critically ill patients improves performance and reduces medical costs [1], [2]. Glucose levels control is a demanding and difficult task for both patients and their families. To keep good levels of blood glucose, the patient must have some capacity of prediction to know what level of glucose would have if ingested a certain amount of food or injected with a quantity of a insulin of a certain kind. In fact, the objective is to avoid not only long periods of hyperglycemia (glucose levels ≥120 mg/dl) but also episodes of severe hypoglycemia (glucose levels ≤ 40 mg/dl) that can lead to patient death.
One of the aspects that make it difficult to control blood glucose level is the lack of a general model of response to both insulin and the various factors mentioned above, due to the particularities of each patient [3]. Models in the literature apply classical modeling techniques, resulting in linear equations, defined profiles, or models with a limited set of inputs. Here we propose a novel technique that involves obtaining the patient model using genetic programming (GP). GP eliminates barriers in building the model, such as linearity or limitations on the input parameters.
Evolutionary techniques such as GP, have certain characteristics that make them particularly suited to address optimization problems and complex modeling. First, they are conceptually simple in its application but have a theoretical basis defined and widely studied. GP has demonstrated its applicability to many real problems, and is intrinsically parallelizable to work with a set of solutions. Furthermore, EAs have great potential to incorporate knowledge about the domain and to incorporate other search mechanisms (not necessarily evolutionary).
One of the best known applications of GP is symbolic regression and the application of one of its variants, Grammatical Evolution (GE), allows to obtain solutions that incorporate non-linear terms. GE is an evolutionary computation technique established in 1998 by Conor Ryan's group at the University of Limerick (Ireland) [4]. GP aims to find an executable program or function that respond to the reference data. The key advantage is that GE applies genetic operators to a whole chain, which simplifies the search application in different programming languages. In addition, there are no memory problems, unlike with GP where the tree representation could have the well know problem of bloating (an excessive growing of the computer structures in memory). Hence, we propose to apply GE to find a custom model that describes and predicts the blood glucose level in a patient. Our method takes the historic data of a patient consisting in previous glucose levels, ingested carbohydrates and injected insulin, and obtains an expression that can be used to predict near future glucose values. The contributions of this work are:
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We propose a method based on GE to obtain individualized and customized glycemia (glucose level in blood) models in humans.
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We have tested this proposal with five in silico patients taken from AIDA simulator [5].
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We present a study of four different grammars and five objective functions.
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We have selected the best models for each patient and run a test phase with a new dataset. In the test phase the models characterized the glucose with a mean percentage average error of 13.69%, reflecting also a good representation of both hyper and hypoglycemic situations.
The rest of the paper is organized as follows. Section 2 describes the related work. Section 3 details how Grammatical Evolution can be applied to this problem. Section 4 shows the general model we propose, as well as the grammars, particular models and objective functions we have studied for the glucose estimation problem. Section 5 is devoted to the experimental setup, while Section 6 presents the results obtained in both training and test phases. Finally, Section 7 explains the conclusions and the future work.
Section snippets
Related work
Glucose level control is a very demanding and difficult task for both patients and their families. Trying to keep a good control of blood glucose involves to perform blood glucose regular measurements (which involves at least one puncture in each measure or using a continuous monitoring system during some periods), insulin dose estimation, carbohydrates estimation, analyze that information somehow and to have some capacity of prediction that allows the patient to know what level of glucose
Evolutionary approach
The aim of this work is to find out an expression to model the glucose level of a diabetic patient. This expression should be obtained from previous collected data of glucose, carbohydrates and insulin. Therefore, we deal with a kind of symbolic regression (SR) Problem. SR tries to obtain a mathematical expression to reproduce a set of discrete data. Genetic Programming GP has proven effective in a number of SR problems, although there are some limitations, which often come in the way of
Model description
A model for glucose levels should be based on observable factors as well as on intrinsic non-observable features of the patient's body. Observable factors are those data that either the patient or a measure machine can collect, while non-observable factors should be inferred. Hence, we propose a model that considers all these factors, applying GE to infer an expression that characterize the behavior of the glucose in diabetic patients. In addition, we describe in this section the different
Experimental setup
In this section we describe the characteristics of the five in silico patients we dealt with, as well as the configuration of each set of experiments.
Results
Our experiments are divided into training and test phases. The objective of the training phase is to evaluate the performance of the proposed grammars in combination with the fitness functions, as well as to obtain models that characterize the glucose behavior on each patient. In this phase, the training dataset is formed by the 24-h records of five in silico patients. We have executed 30 runs with the same configuration of grammar and objective for each patient. Given that we have studied four
Conclusions and future work
In this paper we propose an evolutionary method based on GE that automatically obtains custom models for blood glucose levels in diabetic patients. Up to our knowledge, this is the first proposal where GE is applied to obtain glucose models in diabetics.
The main advantages of our method are: (1) the model is obtained as a custom expression for each patient, which improves the individual treatment of a diabetic person; (2) the training dataset can be easily collected by a patient or by a simple
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