Elsevier

Applied Soft Computing

Volume 77, April 2019, Pages 316-328
Applied Soft Computing

A genetic programming-based regression for extrapolating a blood glucose-dynamics model from interstitial glucose measurements and their first derivatives

https://doi.org/10.1016/j.asoc.2019.01.020Get rights and content

Highlights

  • A regression method for estimating blood glucose from interstitial one is presented.

  • The approach is a early stage in building the basic component of artificial pancreas.

  • The investigation concerns both personalized models and global ones.

  • The discovered models are assessed through a comparison with other well-know models.

Abstract

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.

Introduction

Diabetes mellitus (DM) is a metabolic life-long disease characterized by inadequate control of blood glucose concentration in the body that induces a high (hyperglycemia) or a low (hypoglycemia) blood glucose (BG) level over a prolonged period. The glucose amount in the blood is regulated primarily by two hormones produced by the pancreas, i.e, insulin and glucagon, that indirectly affect the blood glucose concentration by lowering it (insulin) or by increasing it (glucagon). Insulin is essential for the conversion of glucose into energy utilized by cells after a food intake when there is an increase in glucose concentration. In absence of insulin, increased concentration of glucose in blood and interstitial fluid, if left untreated, can entail complications, such as the damage and the eventual failure of certain parts of multiple organs or even graver side effects like an increased risk of cardiac heart dysfunctions and failures, and stroke [1], [2], [3]. Instead the glucagon and hepatic production of glucose prevent the glucose concentration from decreasing substantially between meals or during the sleep. The control of this concentration allows avoiding complications as headache, hunger, difficulty in sleeping or more serious consequences like loss of consciousness, seizure and even coma. All these medical problems have a substantial impact on quality and on expectancy of life.

Diabetes is a worldwide growing phenomenon [4]. Since there is currently no cure, such a disease requires daily care and it is extremely important that the patients learn to effectively manage this condition to enhance their quality of life. Diabetic patients must be informed about the disease, instructed towards an appropriate diet, new hygiene habits, and taught about devised therapy and available medical devices, and drugs.

The diabetes is categorized in three major types: Type 1, Type 2 and gestational diabetes. With DM Type 1, there is a complete lack of insulin as pancreas fails to generate it. With DM Type 2, patient presents an insulin resistance as cells necessitate an increment in insulin to operate appropriately. With gestational diabetes, insulin resistance is coupled with an insulin secretory defect. The insulin secretion is too low to comply with the increased requests activated by the insulin resistance.

Within this paper the focus is on Type-1 DM or insulin-dependent diabetes, characterized by an autoimmune destruction of the insulin produced by the pancreatic β-cells. The patients affected by such a chronic disorder are subject to a progressive insulin deficiency and a resultant hyperglycemia, and are totally dependent on an external injection of insulin to regulate their blood-glucose concentration. This regulation is one of the most challenging control problems to tackle in biomedical engineering. Hence, a methodology able to attain a BG estimation as precise as possible assumes a very crucial role to establish the appropriate rate of insulin to infuse.

Proper treatments to control the blood concentration and prevent the complications associated to high BG levels last for many years and the related social costs are very high.

Several invasive estimation devices are present on the market that take BG measures in intervals that range from about 15 min to a couple of hours with no measurements taken during the night. Patients are reluctant to be subject to this continuous invasive BG control because of the related pain. Hence, it can become difficult to suitably take care of the sick persons. For such a reason, we need a methodology that obtains continuous BG estimations by using minimally invasive devices. This possibility is offered by the minimally invasive Continuous Glucose Monitoring System (CGMS) devices that in a simpler way measure the IG, i.e., the glucose in the subcutaneous tissue [5].

CGMS are portable devices capable of measuring glycemic levels indirectly from the interstitial space almost continuously for several days with a prefixed frequency. However, CGM sensors are affected by distortion due to the glucose diffusion process across capillary wall between blood and interstitial fluid, and by the time-by-time-varying systematic under/over-estimations due to calibrations, sensor drifts and measurement noise [6], [7]. Most of these devices need to be calibrated — to convert the measured electric current to glucose level. Patient has to calibrate at least two times a day, when BG and IG are steady. At this time, both levels can be considered as equal and thus CGMS knows what quantity of electric current equals BG. Despite the fact that more and more accurate devices are explored [8], [9], errors in sensors calibration cause the measure inaccuracy of CGMS with respect to BG.

Although IG is not reckoned as a perfect BG indicator, nevertheless it is the only system that permits large number of continuous and non-invasive measurements a day. However, the complexity of the relationship between glucose dynamics in BG and IG is far too complex to be acquired by the calibration algorithms relying on simple linear regression techniques implemented in current CGMS devices [10], [11]. In fact, CGMS is a low-power device that implies low computational capacities and this invalidates the accuracy of the measurements.

Considered that BG and IG can be significantly different due to physiological reasons, the availability of a large amount of IG measures is highly advisable to acquire as much as possible of the BG-to-IG dynamics. In fact, significant progresses with CGMS and insulin pumps have allowed CGMS data to be utilized to regulate insulin delivery [12].

Several analytical models have been suggested attempting to infer a mathematical relationship of IG and BG, as shown in Section 2. All these models represent a basic step to design and implement an artificial pancreas (AP) [13], i.e., an artificial device capable of automatically regulating insulin injections according to the patients’ needs so to ensure them a satisfactory quality of life. This device must be capable of performing a glycemic control by estimating BG values through the analysis of the IG signal. Reliable prediction based on IG only is still beyond the reach since current algorithms are based on supplemental, defective information such as an assessment of carbohydrate intake by the patient.

In our previous work we have presented a modeling approach able to estimate BG levels based on the measurements of IG time series values [14]. In the present work the inferred models rely on the measurements of IG and their numerical first derivatives, and such an approach is adopted to explore a patient-oriented approach in addition to a general model. Moreover, a more thorough review of the related works and additional experimentations are included with respect to a seminal conference paper [15].

The aim is to discover a law able to estimate BG values by using IG measurements and their numerical first derivatives. This law could be the core of the knowledge base of an AP. These estimation problems are known as regression problems. The induction of an analytical model for this kind of problems is a very complex task given the nonlinear nature of the relationship between the input and the output variables. The evolutionary computation techniques have been proved able in dealing with the modeling of nonlinear processes in many fields [16], [17], [18], [19], [20]. Considered the complexity of inducing an analytical model, we leverage the ability of the Genetic Programming (GP) [21] in tackling regression problems [22] to detect an efficient approximation of the relationship between BG and IG values and their numerical first derivatives. The experimental phase is carried out over a real-world database including both BG and IG measures for several Type-1 diabetic subjects.

The paper is organized as follows. In Section 2 a review of the relevant related work is given. Section 3 describes the proposed genetic-based approach. A discussion and a comparison with other models on the results attained on personalized and global data is shown in Section 4. Conclusions and future work are exposed in Section 5.

Section snippets

Related research

Numerous mathematical, statistical and analytical models focused on different aspects of diabetes, ranging from molecular and cellular biology, to clinical science and to health service research have been developed [23], [24], [25]. These approaches can be broadly subdivided in three groups: physiological, hybrid and data-based models.

Physiological models. Hovorka et al. [26] developed a nonlinear predictive model to preserve normoglycemic Type-1 diabetic patients during fasting conditions such

The proposed approach

A GP-based approach for estimating BG levels in diabetic patients starting from their IG measurements and their corresponding numerical first derivatives is devised for solving such a problem known as a symbolic regression problem.

The proposed approach relies on the structure of the SR model, that is the first and most widely used model trying to relate BG with IG and IG derivative [41]. Nevertheless, there exist situations in which the SR model does not precisely hold, for example in case of

Experimental findings

The experimentation phase has been carried out following the three-step procedure described in detail at the beginning of Section 3, i.e., database enrichment, numerical first derivative computation and model extraction.

We have subdivided our experiments into two parts. In the former, we have used a personalized approach, so that the goal has been to find the best model for all the subjects by using the enriched data set with interpolation as described in Section 3.1. The relative results are

Conclusions and future works

The present paper has introduced an innovative evolutionary methodology for estimating BG from IG measurements and their numerical first derivatives. Specifically, through the GP, the proposed approach derives a law able to forecast the BG trend of diabetic subjects by starting from their past BG and IG measurements. To demonstrate the effectiveness of this method, several experiments have been carried out over a real-world database containing both BG and IG measurements from five diabetic

Acknowledgments

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

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