Modeling glycemia in humans by means of Grammatical Evolution

doi:10.1016/j.asoc.2013.11.006

Applied Soft Computing

Volume 20, July 2014, Pages 40-53

https://doi.org/10.1016/j.asoc.2013.11.006 Get rights and content

Highlights

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We propose a method based on Grammatical Evolution to obtain individualized and customized glycemia models in humans.
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We have tested this proposal with five in silico patients taken from AIDA simulator.
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We present a study of four different grammars and five objective functions.
•
In the test phase GE-models characterized glucose levels with a mean percentage average error of 13.69%.
•
Models obtained with our method reflect also a good representation of both hyper and hypoglycemic situations.

Abstract

Diabetes mellitus is a disease that affects to hundreds of millions of people worldwide. Maintaining a good control of the disease is critical to avoid severe long-term complications. In recent years, several artificial pancreas systems have been proposed and developed, which are increasingly advanced. However there is still a lot of research to do. One of the main problems that arises in the (semi) automatic control of diabetes, is to get a model explaining how glycemia (glucose levels in blood) varies with insulin, food intakes and other factors, fitting the characteristics of each individual or patient. This paper proposes the application of evolutionary computation techniques to obtain customized models of patients, unlike most of previous approaches which obtain averaged models. The proposal is based on a kind of genetic programming based on grammars known as Grammatical Evolution (GE). The proposal has been tested with in silico patient data and results are clearly positive. We present also a study of four different grammars and five objective functions. In the test phase the models characterized the glucose with a mean percentage average error of 13.69%, modeling well also both hyper and hypoglycemic situations.

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:

•
We propose a method based on GE to obtain individualized and customized glycemia (glucose level in blood) models in humans.
•
We have tested this proposal with five in silico patients taken from AIDA simulator [5].
•
We present a study of four different grammars and five objective functions.
•
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

References (28)

F. Stahl et al.
Diabetes mellitus modeling and short-term prediction based on blood glucose measurements
Math. Biosci.
(2009)
R. Hovorka et al.
Manual closed-loop insulin delivery in children and adolescents with type 1 diabetes: a phase 2 randomised crossover trial
Lancet
(2010)
L. Magni et al.
Model predictive control of glucose concentration in type i diabetic patients: an in silico trial
Biomed. Signal Process. Control
(2009)
D.E. Rivera et al.
Systematic techniques for determining modelling requirements for siso and mimo feedback control
J. Process Control
(1995)
H. Lee et al.
A closed-loop artificial pancreas based on model predictive control: human-friendly identification and automatic meal disturbance rejection
Biomed. Signal Process. Control
(2009)
International surviving sepsis campaign guidelines committee: surviving sepsis campaign: international guidelines for management of severe sepsis and septic shock
Crit. Care Med.
(2008)
J. Krinsley et al.
Cost analysis of intensive glycemic control in critically ill adult patients
Chest
(2006)
American Diabetes Association
Standards of medical care in diabetes 2010
Diabetes Care
(2010)
C. Ryan et al.
Grammatical evolution: evolving programs for an arbitrary language
AIDA diabetic software simulator, URL...

K. van Heusden et al.

Control-relevant models for glucose control using a priori patient characteristics

IEEE Trans. Biomed. Eng.

(2012)

C. Cobelli et al.

Diabetes: models, signals, and control

IEEE Rev. Biomed. Eng.

(2009)

D.A. Finan et al.

Effect of input excitation on the quality of empirical dynamic models for type 1 diabetes

AIChE J.

(2009)

F. El-Khatib et al.

A bihormonal closed-loop artificial pancreas for type 1 diabetes

Sci. Transl. Med.

(2010)

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Recent trends and techniques of blood glucose level prediction for diabetes control
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Diabetes, a metabolic disorder disease, can cause short-term acute or even long-term chronic complications in a patient’s body. In 2021, 10.5% of the world’s adult population had diabetes. These numbers are increasing day by day, which results in an associated increase of morbidity, mortality, and health care cost related to diabetes. Thus, a huge research effort has been carried out to manage diabetes. A precursor to diabetes management is to predict the future blood glucose levels based on a patient’s past history. In this paper, we provide a comprehensive and systematic study of diabetes management, focusing on recent research towards blood glucose level prediction. In particular, we have categorized and presented existing recent research based on major clinical application domains, different input features, and major modeling techniques including physiological, data-driven, and hybrid models. We have summarized the performance analysis of different modeling techniques using different metrics, and critically analyzed these techniques from different perspectives. Finally, we have identified a number of research challenges and potential future works that range from data collection to model improvement for Type 2 Diabetes Mellitus. This review can be a good starting point for researchers and practitioners who are working in building data-driven computational models for diabetes management and blood glucose level prediction.
Reducing high-risk glucose forecasting errors by evolving interpretable models for Type 1 diabetes
2023, Applied Soft Computing
Diabetes mellitus is a metabolic disease involving high blood glucose levels that can lead to serious medical consequences. Hence, for diabetic patients the prediction of future glucose levels is essential in the management of the disease. Most of the forecasting approaches in the literature evaluate the effectiveness of glucose predictors only with numerical metrics. These approaches are limited because they evenly treat all the errors without considering their different clinical impact that could involve lethal effects in dangerous situations such as hypo- or hyperglycemia.
To overcome such a limitation, this paper aims to devise models for reducing high-risk glucose forecasting errors for Type 1 diabetic patients. For this purpose, we exploit a Grammatical Evolution algorithm to induce personalized and interpretable forecasting glucose models assessed with a novel, composite metric to satisfy both clinical and numerical requirements of the estimated predictions.
To assess the effectiveness of the proposed approach, a real-world data set widely used in literature, consisting of data from several patients suffering from Type 1 diabetes, has been adopted. The experimental findings show that the induced models are interpretable and capable of assuring predictions with a good tradeoff between medical quality and numerical accuracy and with remarkable performance in reducing high-risk glucose forecasting errors. Furthermore, their performance is better than or comparable to that of other state-of-the-art methods.
Data-driven modeling and prediction of blood glucose dynamics: Machine learning applications in type 1 diabetes
2019, Artificial Intelligence in Medicine
Citation Excerpt :
The two most used variants of EA in BG prediction and modeling approaches are genetic programming (GP) and genetic algorithms (GA). Hidalgo et al. [76,77] used a genetic programming-based symbolic regression known as grammatical evolution to develop an individualized model of BG dynamics. Moreover, Contreras et al. [71] used the grammatical evolution approach to develop a standalone BG prediction model.
Diabetes mellitus (DM) is a metabolic disorder that causes abnormal blood glucose (BG) regulation that might result in short and long-term health complications and even death if not properly managed. Currently, there is no cure for diabetes. However, self-management of the disease, especially keeping BG in the recommended range, is central to the treatment. This includes actively tracking BG levels and managing physical activity, diet, and insulin intake. The recent advancements in diabetes technologies and self-management applications have made it easier for patients to have more access to relevant data. In this regard, the development of an artificial pancreas (a closed-loop system), personalized decision systems, and BG event alarms are becoming more apparent than ever. Techniques such as predicting BG (modeling of a personalized profile), and modeling BG dynamics are central to the development of these diabetes management technologies. The increased availability of sufficient patient historical data has paved the way for the introduction of machine learning and its application for intelligent and improved systems for diabetes management. The capability of machine learning to solve complex tasks with dynamic environment and knowledge has contributed to its success in diabetes research.
Recently, machine learning and data mining have become popular, with their expanding application in diabetes research and within BG prediction services in particular. Despite the increasing and expanding popularity of machine learning applications in BG prediction services, updated reviews that map and materialize the current trends in modeling options and strategies are lacking within the context of BG prediction (modeling of personalized profile) in type 1 diabetes.
The objective of this review is to develop a compact guide regarding modeling options and strategies of machine learning and a hybrid system focusing on the prediction of BG dynamics in type 1 diabetes. The review covers machine learning approaches pertinent to the controller of an artificial pancreas (closed-loop systems), modeling of personalized profiles, personalized decision support systems, and BG alarm event applications. Generally, the review will identify, assess, analyze, and discuss the current trends of machine learning applications within these contexts.
A rigorous literature review was conducted between August 2017 and February 2018 through various online databases, including Google Scholar, PubMed, ScienceDirect, and others. Additionally, peer-reviewed journals and articles were considered. Relevant studies were first identified by reviewing the title, keywords, and abstracts as preliminary filters with our selection criteria, and then we reviewed the full texts of the articles that were found relevant. Information from the selected literature was extracted based on predefined categories, which were based on previous research and further elaborated through brainstorming among the authors.
The initial search was done by analyzing the title, abstract, and keywords. A total of 624 papers were retrieved from DBLP Computer Science (25), Diabetes Technology and Therapeutics (31), Google Scholar (193), IEEE (267), Journal of Diabetes Science and Technology (31), PubMed/Medline (27), and ScienceDirect (50). After removing duplicates from the list, 417 records remained. Then, we independently assessed and screened the articles based on the inclusion and exclusion criteria, which eliminated another 204 papers, leaving 213 relevant papers. After a full-text assessment, 55 articles were left, which were critically analyzed. The inter-rater agreement was measured using a Cohen Kappa test, and disagreements were resolved through discussion.
Due to the complexity of BG dynamics, it remains difficult to achieve a universal model that produces an accurate prediction in every circumstance (i.e., hypo/eu/hyperglycemia events). Recently, machine learning techniques have received wider attention and increased popularity in diabetes research in general and BG prediction in particular, coupled with the ever-growing availability of a self-collected health data. The state-of-the-art demonstrates that various machine learning techniques have been tested to predict BG, such as recurrent neural networks, feed-forward neural networks, support vector machines, self-organizing maps, the Gaussian process, genetic algorithm and programs, deep neural networks, and others, using various group of input parameters and training algorithms. The main limitation of the current approaches is the lack of a well-defined approach to estimate carbohydrate intake, which is mainly done manually by individual users and is prone to an error that can severely affect the predictive performance. Moreover, a universal approach has not been established to estimate and quantify the approximate effect of physical activities, stress, and infections on the BG level. No researchers have assessed model predictive performance during stress and infection incidences in a free-living condition, which should be considered in future studies. Furthermore, a little has been done regarding model portability that can capture inter- and intra-variability among patients. It seems that the effect of time lags between the CGM readings and the actual BG levels is not well covered. However, in general, we foresee that these developments might foster the advancement of next-generation BG prediction algorithms, which will make a great contribution in the effort to develop the long–awaited, so-called artificial pancreas (a closed-loop system).
A genetic programming-based regression for extrapolating a blood glucose-dynamics model from interstitial glucose measurements and their first derivatives
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Citation Excerpt :
Hybrid models. Hidalgo et al. [31] incorporated medical knowledge into a grammar evolution approach aimed to derive an expression for glucose that considered previous BG values, carbohydrate intake, and insulin administration. This incorporation involved exploring four different grammars and five fitness functions, all of which were evaluated with respect to average error as a performance metric for all patients.
This paper illustrates the development and the applicability of an Evolutionary Computation approach to enhance the treatment of Type-1 diabetic patients that necessitate insulin injections. In fact, being such a disease associated to a malfunctioning pancreas that generates an insufficient amount of insulin, a way to enhance the quality of life of these patients is to implement an artificial pancreas able to artificially regulate the insulin dosage. This work aims at extrapolating a regression model, capable of estimating the blood glucose (BG) through interstitial glucose (IG) measurements and their numerical first derivatives. Such an approach represents a viable preliminary stage in building the basic component of this artificial pancreas. In particular, considered the high complexity of the reciprocal interactions, an evolutionary-based strategy is outlined to extrapolate a mathematical relationship between BG and IG and its derivative. The investigation is carried out about the accuracy of personalized models and of a global relationship model for all of the subjects under examination. The discovered models are assessed through a comparison with other models during the experiments on personalized and global data.
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IMPROVING ALGEBRAIC EXPRESSION GENERATION USING CROW SEARCH BASED GENETIC ALGORITHM
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Modeling glycemia in humans by means of Grammatical Evolution

Highlights

Abstract

Graphical abstract

Introduction

Section snippets

Related work

Evolutionary approach

Model description

Experimental setup

Results

Conclusions and future work

Math. Biosci.

Lancet

Biomed. Signal Process. Control

J. Process Control

Biomed. Signal Process. Control

International surviving sepsis campaign guidelines committee: surviving sepsis campaign: international guidelines for management of severe sepsis and septic shock

Crit. Care Med.

Cost analysis of intensive glycemic control in critically ill adult patients

Chest

Standards of medical care in diabetes 2010

Diabetes Care

Grammatical evolution: evolving programs for an arbitrary language