Genetic Programming-based induction of a glucose-dynamics model for telemedicine

https://doi.org/10.1016/j.jnca.2018.06.007Get rights and content

Highlights

  • The paper outlines precursory steps for a deployment of a remote portal for diabetes.

  • A regression model to estimate the blood glucose by interstitial glucose is derived.

  • A new evolutionary technique to estimate the missing blood glucose values is devised.

  • The model discovered is compared with other models on global and personalized data.

  • The estimation of blood glucose clinically validated will be added to the web portal.

Abstract

This paper describes our preliminary steps towards the deployment of a brand-new original feature for a telemedicine portal aimed at helping people suffering from diabetes. In fact, people with diabetes necessitate careful handling of their disease to stay healthy. As such a disease is correlated to a malfunction of the pancreas that produces very little or no insulin, a way to enhance the quality of life of these subjects is to implement an artificial pancreas able to inject an insulin bolus when needed. The goal of this paper is to extrapolate a regression model, capable of estimating the blood glucose (BG) through interstitial glucose (IG) measurements, that represents a possible revolutionizing step in constructing the fundamental element of such an artificial pancreas. In particular, a new evolutionary approach is illustrated to stem a mathematical relationship between BG and IG. To accomplish the task, an automatic evolutionary procedure is also devised to estimate the missing BG values within the investigated real-world database made up of both BG and IG measurements of people suffering from Type 1 diabetes. The discovered model is validated through a comparison with other models during the experimental phase on global and personalized data treatment. Moreover, investigation is performed about the accuracy of one single global relationship model for all the subjects involved in the study, as opposed to that obtained through a personalized model found for each of them. Once this research is clinically validated, the important feature of estimating BG will be added to a web portal for diabetic subjects for telemedicine purposes.

Introduction

Diabetes mellitus (DM) is a lifelong disease that causes a high level of blood glucose (BG). The amount of glucose in the blood is controlled by the insulin hormone produced by the pancreas. Insulin lowers BG by promoting glucose utilization by cells. Without insulin, glucose accumulates in various compartments. Subsequently, it binds to certain parts of multiple organs, thus damaging them and eventually leading to their failure.

Let us briefly describe diabetes pathogenesis with Type 1, Type 2 and gestational diabetes. With Type 1 DM, there is an absolute lack of insulin as pancreas fails to produce it. With Type 2 DM, patient exhibits insulin resistance as cells need an increased amount of insulin to work properly. With gestational diabetes, insulin resistance is coupled with insufficient insulin secretion. The insulin secretion is too low to satisfy the increased requirements triggered by insulin resistance.

Over time, having too much glucose in the blood can cause serious medical problems ranging from retinopathy, neuropathy, and nephropathy or even graver side effects such as an increased risk of heart disease and stroke (World Health Organization, 2013). The diabetes has no cure and is spreading at alarming level across a large portion of the world population. Fortunately it is possible to improve the quality of life of the patients by controlling the medical risks associated to high BG levels through adequate treatments. These treatments last for many years and are very expensive for the society. Therefore, a methodology able to obtain an as precise as possible BG estimate to establish the right amount of insulin to inject assumes a very important role.

Another key point is the patient's education. Diabetic patients must be educated about the disease, redesigned diet, new hygiene habits, drugs, devised therapy and available medical devices. Moreover, diabetic subjects may live far from doctors, or may have impairment in their movements due to problems to feet caused by this disease, or doctors may have not too much time to suitably follow all of their patients. All these issues call for remote management. It is possible to partially offload these issues using telemedicine. Specifically, it is possible to create a specialized web portal for diabetic patients. In fact, several such portals already exist. These portals can be classified into three, possibly overlapping, categories:

  • 1.

    informative: informative portals provide general advices to diabetic patients about diet, hygiene habits, medical devices, etc., but they offer no glucose-signal processing;

  • 2.

    glucometer-oriented: these portals can include general advices along with the possibility to upload and visualize glucose measurements;

  • 3.

    advanced glucose-signal processing: on top of the functionality of the previous two portal categories, portals in this category are capable of calculating a new glucose signal from the measured glucose signal. For example, such a portal can calculate continuous BG from continuous interstitial glucose (IG) measurements. The portal requires a model of glucose dynamics to operate, because its processing goes beyond a simple processing of the glucose signal to produce a statistics summary and to visualize the signal itself.

Informative portals are easy to find and several glucometer-oriented portals exist as well. They are usually associated with specific software that downloads data from the meters. Nevertheless, to the best of our knowledge, we are aware about only one portal that offers advanced glucose-signal processing (Koutny et al., 2016). This portal is an innovative tool and we are committed to its further development, for which we need to keep researching new ways to derive highly personalized models of glucose dynamics - which is the aim of this paper.

As a face-to-face interaction between patient and physician becomes costly since it requires physician's time, telemedicine, a specialized web portal in our case, becomes an important tool along with the medical devices as reported in Section 3.

Several estimation devices present on the market take BG measures in intervals ranging from about 15 min to a couple of hours with no measurements acquired during the night. Since most of these devices are invasive, patients are reluctant to be subject to this continuous and invasive BG control because of the associated pain. Hence, it can become difficult to adequately take care of the patients. Instead there is the possibility of measuring more simply the IG, i.e., the glucose in the subcutaneous tissue, through the minimally invasive and easier-to-use Continuous Glucose Monitoring System (CGMS) devices (Vashist, 2013). With CGMSs, a needle is inserted into subcutaneous tissue to measure electric current in the interstitial fluid of that tissue. A glucose-triggered reaction produces the current.

CGMSs can be programmed to take measures with a prefixed frequency for a number of days, also during the night. Nevertheless, a CGMS needs BG to calibrate - to transform the measured electric current to glucose level. A patient needs to calibrate at least two times a day, when BG and IG are steady. While the patient collects only a few BGs, a CGMS can provide hundreds of measurements a day.

Considered that BG and IG can differ considerably due to physiological reasons, the availability of a large amount of IG measures is highly recommendable to capture as much of the BG-IG dynamics as possible. Then, it is possible to derive a precise estimation of BG by exploiting the availability of a large amount of IG measures for taking care of patients.

Although IG is not considered a perfect indicator for BG, nonetheless it is the only one to be available with continuous and non-invasive measurements. However, the complexity of the relationship between glucose dynamics in BG and IG is far too complex to be captured in the very simple calibration algorithms implemented in CGMS devices available in the market (Baek et al., 2010; Rossetti et al., 2010). In fact, a CGMS is a low-power device that implies low computational capabilities and this could invalidate the accuracy of the measurements.

In the literature, different analytical models have been presented attempting to derive a mathematical relationship of IG and BG, as reported in Section 2. All these models represent a basic step to design and implement an artificial pancreas, i.e., an artificial device capable of automatically regulating insulin injections according to the needs so to assure an as-normal-as-possible life to patients. This device must be able to carry out a glycemic control by estimating BG values through the analysis of the IG signal. Reliable prediction based on IG only it is still out of reach and present algorithms must rely on supplementary, imperfect information such as an assessment of carbohydrate intake by the patient.

The paper is a revised and extended version of a conference paper (De Falco et al., 2018). In particular, a more thorough review of the research contribution in terms of related works and of a description of a web portal for telemedicine along with additional experimentations are included. This paper provides a twofold contribution. The first one is the introduction of an innovative evolutionary technique to exert new BG values without performing further measurements. Such a strategy allows increasing the number of the BG values included in the database, which is a critical problem when searching for a prediction model. The second contribution consists in leveraging this modified database to symbolically derive a law able to estimate BG values by using IG measurements. These estimation problems are known as regression problems. Considering their complexity, we exploit the capability of the Genetic Programming (GP) (Koza, 1992) in tackling regression problems (Borrelli et al., 2006) to find a good and effective approximation of the relationship between IG and BG values. The experimental trials are performed over a real-world database containing both BG and IG measures for several subjects suffering from Type 1 DM. The aim is to discover an explicit relationship, i.e., a mathematical expression, between BG and IG values that could be the core of the knowledge base of an artificial pancreas.

An important question our paper wishes to tackle is whether or not a global approach leading to one single general model for a given set of subjects can be competitive with respect to the results obtained by finding a specific model for each of the subjects involved in the study. This is significant, because, of course, the personalized approach has the cost of needing learning over each subject. Learning needs a preliminary phase of data gathering from the subject, followed by sending this data to GP experts who have to run the algorithm and find the model for that subject, then add it to the measurement device to be given for the subject under account to use.

The paper is organized as follows. In Section 2 a review of the relevant related work is given. As a telemedicine tool, a specialized and interactive web portal for diabetic patients is introduced in Section 3. Section 4 outlines the strategy employed, along with an innovative evolutionary procedure to enlarge the original database presenting too many missing BG values in Section 4.1, and the genetic-based regression model in Section 4.2. A comparison with other models on the results obtained both on global and personalized data treatment is reported in Section 5. In the same section, we compare the results achieved with the global and the personalized approaches, and discuss the outcome of such experiments. Conclusions and future work are exposed in Section 6.

Section snippets

Related research

Several analytical models have been introduced with the aim to find a mutual relationship between BG and IG values.

The first, and most widely used, model attempting to relate BG and IG was devised in (Rebrin et al., 1999). It is represented by the following equation:τgdi(t)dt+1gi(t)=b(t)where b(t) and i(t) are the BG and the IG at time t, and the parameters g and τ represent the steady-state gain and the IG equilibration time constant, respectively. An important task is the estimation of the

The web portal

Telemedicine makes use of information and telecommunication technologies to deliver health care remotely. In such a way a patient receives the medical care without physically visiting a physician. Chronic illnesses - like a diabetes mellitus - require lifetime compliance from the patient and every method which decreases consumption of time “for disease” is beneficial. Travel expenses are also significant. Moreover, it may be difficult to reach the physician if the patient has already developed

The evolutionary methodology

The evolutionary methodology proposed within this paper can be summarized in two basic steps: i) the use of an evolutionary optimizer to evaluate the model parameters to define an automatic procedure that allows enriching the original database with estimated BG values; ii) the extraction of an explicit symbolic regression model by exploiting an appropriate evolutionary technique, i.e., a GP algorithm.

The database

From the Diabetology Center at the Pilsen University Hospital, we received anonymized datasets of Type-1 diabetic patients. We transformed the datasets into a database. The database comprises 5 different patients, their IDs being 1, 2, 4, 5, and 6, respectively. It is to note that the subject with ID 3 was excluded due to anomalies in the collected data. Each patient comprises several time segments. A time segment is a period during which the patient has worn a CGMS. There are 9, 30, 31, 38 and

Conclusions

The main problem for a regression model in finding a relationship between variables is the absence of a sufficient number of values of the variables to be correlated. This is the usual situation in the research area of diabetes where the easily available number of IG values contrasts with the low number of corresponding number of measured BG values. Within this paper, to overcome the problem, we have envisaged an evolutionary procedure to enrich the database made up of many missing BG values by

Acknowledgements

This publication was partially supported by the project LO1506 of the Czech Ministry of Education, Youth and Sports.

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