A signal processing application for evaluating self-monitoring blood glucose strategies in a software agent model

Highlights

• A cross-correlation function and an average deviation between the continuous blood glucose and the interpolation of limited blood glucose samples are calculated.

• This model evaluates blood glucose monitoring frequency in a self-aware patient software agent model.

• This model provides diabetes patients and physicians a good understanding of the illness from limited blood glucose samples.

• We propose a new way to determine an appropriate blood glucose monitoring frequency to reduce the cost and discomfort associated with blood glucose monitoring.

• We propose a base line to assist people to determine an individual appropriate monitoring frequency based on their situations.

Abstract

We propose the signal processing technique of calculating a cross-correlation function and an average deviation between the continuous blood glucose and the interpolation of limited blood glucose samples to evaluate blood glucose monitoring frequency in a self-aware patient software agent model. The diabetic patient software agent model [1] is a 24-h circadian, self-aware, stochastic model of a diabetic patient's blood glucose levels in a software agent environment. The purpose of this work is to apply a signal processing technique to assist patients and physicians in understanding the extent of a patient's illness using a limited number of blood glucose samples. A second purpose of this work is to determine an appropriate blood glucose monitoring frequency in order to have a minimum number of samples taken that still provide a good understanding of the patient's blood glucose levels. For society in general, the monitoring cost of diabetes is an extremely important issue, and these costs can vary tremendously depending on monitoring approaches and monitoring frequencies. Due to the cost and discomfort associated with blood glucose monitoring, today, patients expect monitoring frequencies specific to their health profile. The proposed method quantitatively assesses various monitoring protocols (from 6 times per day to 1 time per week) in nine predefined categories of patient agents in terms of risk factors of health status and age. Simulation results show that sampling 6 times per day is excessive, and not necessary for understanding the dynamics of the continuous signal in the experiments. In addition, patient agents in certain conditions only need to sample their blood glucose 1 time per week to have a good understanding of the characteristics of their blood glucose. Finally, an evaluation scenario is developed to visualize this concept, in which appropriate monitoring frequencies are shown based on the particular conditions of patient agents. This base line can assist people in determining an appropriate monitoring frequency based on their personal health profile.

Introduction

Diabetes is fast becoming an epidemic in today's society. The International Diabetes Federation estimates that, in 2012, over 371 million people suffered from diabetes and 4.8 million people died [2]. In addition, diabetes causes a significant financial burden to individuals as well as to society, e.g., diabetes healthcare costs were estimated around 471 billion US dollars in 2012 [2].

Self-monitoring of blood glucose (SMBG) proved to be very effective in terms of blood glucose (BG) control in Type 1 and Type 2 diabetes, alongside insulin treatment [3], [4]. However, whether SMBG improves BG control for Type 2 diabetic patients in the absence of insulin remains controversial [5]. Some researchers believe that SMBG does assist these patients in managing their BG levels [6], [7]. Diabetic patients are better informed of their BG levels through regularly sampling their BG, which leads to better lifestyle decisions including diet control, exercise, and medication [8]. The likelihood of complications is reduced with good BG balance, which can be obtained through frequent SMBG. Furthermore, some of the discomfort associated with hyper- and hypo-glycemia, as well as of repeated finger-prick testing, can be avoided with frequent SMBG [9]. Some other researchers are of the opposite opinion, believing that SMBG is a waste of money [10]. Nonetheless, SMBG has significant potential benefits and is commonly recommended to diabetic patients of both types [6], [7]. According to the recommendations of the American Diabetes Association (ADA) [11], SMBG should be utilized to achieve the optimal postprandial glycemic target. For instance, it is recommended that patients on intensive insulin therapy sample their BG at least 3 times per day [11].

There are several methods of BG monitoring available to diabetic patients today. In certain situations, patients are required to use an invasive continuous glucose monitor which reports BG every 5 min, while most other, patients are asked to use an external blood test using a finger prick and a BG sensitive strip. For the medical community as well as society in general, monitoring costs are an important issue; additionally, they vary tremendously depending on monitoring approaches and monitoring frequencies. Continuous glucose monitors can only be put in place for a limited number of days, and though BG strips are much less expensive, even their costs mount with many samples per day over many months. For instance, the National Health Service (NHS) spends approximately 40% more on materials used for testing BG in diabetic patients than on oral hypoglycemic drugs [12]. In addition, the necessary frequency of SMBG can vary according to the individual patient. Given the cost and discomfort associated with SMBG, it seems appropriate that effort be directed toward the determination of an appropriate SMBG rate for patients. The conventional approach of a Randomized Controlled Trial (RCT) in vivo has obvious disadvantages for determining this appropriate sampling rate, as it is time-consuming, has a significant monetary cost, and is limited by inherent difficulties in the study of unique events.

The BG signal is a complex signal whose values continuously change as a result of numerous patient factors, including health condition, age, exercise, medication, time of day, food intake, lifestyle, etc. The BG signal can be characterized as non-stationary [13] because its fundamental statistics change as a function of time based on conditions experienced by the patients, for example, the consumption of a glucose bolus as a result of eating carbohydrate-rich foods. As a result of its non-stationary quality, periodic sampling of the BG signal is less effective than event-driven sampling. Typically, the patient is advised to record BG levels before and sometime after consumption of a meal. This allows the physician to assess the change in BG values as a result of fasting between meals and due to the meal itself. This variation of BG levels is a useful indicator of the extent of the illness of the patient.

We propose a signal analysis technique of calculating the cross-correlation function and the average deviation (AVD) between continuous blood glucose (CBG) and the interpolation of samples to evaluate BG monitoring frequency (MF) using the self-aware patient agent (SPA) model [14]. This model has been developed to study various aspects of the treatment of diabetic patients. The SPA is a 24-h circadian, self-aware, stochastic model of diabetes, which produces the CBG signal in a mobile agent environment [1]. We extend the original seminal work of Ackerman et al. [15] in creating a mathematical model of human BG levels in three aspects: (1) We incorporate the stochastic and unpredictable effects of daily living; (2) we extend the Ackerman model into the period of night-time; (3) patients’ awareness of their own conditions is incorporated. The SPA has a distinct advantage over human testing, as the ethical issues of patient well-being do not need to be considered.

Ackerman et al. proposed a linearized mathematical model to evaluate glucose-tolerance and BG regulation in the 1960s [15], [16]. It was originally used to predict a combination of sine and exponential wave response to oral glucose consumption in order to characterize the human glucose regulatory system. While there have been significantly more complex (glucose–insulin reactive) models developed since the advent of the Ackerman model, these models rely on more in-depth knowledge and measurement of the metabolic process, which is, in general, not available to the typical diabetic patient on an on-going basis. The Ackerman model is defined by a set of differential equations, and the solution has the form as follows:

$$x(t)=G_0+\frac{F}{\omega }{e}^{-\beta t/2}\sin \omega t$$

where x is the BG level as a function of time t, G₀ is the fasting BG, ω is the natural frequency of the system, β is measured based on the intensity of exercise and medication, and F is a measure of food intake. Their aim was to improve the distinction between normal and abnormal glucose regulation. Ackerman's work has led to significant follow-up research, including the study of Jansson et al. [17] in which Ackerman's model was used to analyze the BG curves obtained during the oral glucose tolerance test in 378 cases. An oral glucose tolerance test measures the body's ability to use glucose. The intestinal glucose re-absorption levels were observed using Ackerman's model to improve the distinction of a diabetic condition from a normal state. Following that, Wu [18] used Ackerman's model to evaluate the degree of diabetes in a particular subject and this subject's response to medications. Wu attempted to define the effect of the medication in terms of parameter fitting of BG measured from a diabetic subject with or without medication. He attempted to assess the impact of the medication based on the values of the parameters in Ackerman's model. Most recently, the Ackerman model was used by Shiang [19] in 2010; their study aimed to develop methods to interpret laboratory glucose and insulin data from glucose tolerance tests, as well as to enhance the Ackerman model.