Article pubs.acs.org/IECR
Fuzzy-Logic-Based Supervisor of Insulin Bolus Delivery for Patients with Type 1 Diabetes Mellitus Shih-Wei Liu,† Hsiao-Ping Huang,† Chia-Hung Lin,‡ and I-Lung Chien*,† †
Department of Chemical Engineering, National Taiwan University, Taipei 10617, Taiwan Division of Endocrinology and Metabolism, Department of Internal Medicine, Chang Gung Memorial Hospital, Tao-Yuan 33305, Taiwan
‡
S Supporting Information *
ABSTRACT: In this article, a fuzzy-logic-based supervisor of insulin bolus delivery for type 1 diabetes mellitus (T1DM) is proposed. The proposed supervisor incorporates expert knowledge into three phases, including recall, inference, and learning phases. A recently developed and well-acknowledged meal simulation model of the glucose−insulin system for T1DM was employed to create virtual subjects for testing. Data from virtual subjects were used to identify an intermediate physiological model, and then our proposed supervisor was synthesized based on this intermediate model. The key features of this fuzzy-logicbased supervisor are that the implementation does not need an online model and it can gradually be updated meal-by-meal. In addition, only two blood glucose measurements between each meal are needed for updating the insulin bolus delivery. The simulation results show that effective and robust glycemic control performance can be achieved. This methodology can be widely applied to patients with continuous subcutaneous insulin infusion (CSII) or multiple daily injections (MDI). predictive control (MPC)1−14 or H∞ control,15−18 are effective methods for meliorating glycemic control. On the other hand, patients under MDI therapy have many fewer BG measurements in a day. Implementing an automatic control algorithm to improve the BG control performance of MDI subjects would be difficult. In this case, a human-like fuzzy-logic supervisor to provide adequate recommendations of bolus injection is a more logical choice. In the control theory field, fuzzy logic has emerged as a promising tool for incorporating expert knowledge and control algorithms and could be a prospective theory to develop a strategy for improving MDI therapy. Some works in the past have employed fuzzy-based strategies to control or regulate the insulin−glucose system for T1DM.19−23 In general, to develop a suitable control strategy, several experiments should be conducted to gain expert knowledge. However, experiments applied to a T1DM patient could cause him or her suffer or could even cause lethal accidents. Thus, a physiological model of the patient is preferred to mimic the real patient for this purpose. To test a proposed control strategy, animal tests have traditionally been applied in preclinical tests. Currently, simulation-based tests can be used to substitute for animal tests.9,10 A number of modelbased algorithms for T1DM patients have been developed.24−28 Balakrishnan et al.29 reviewed and analyzed quite a few of the available BG models for T1DM patients. In our work, we use the glucose metabolism model of Dalla Man and colleagues30,31 as the simulated patients. This model is the core of the closed-loop metabolic simulator6 from University of Virginia (UVA), which was accepted by the U.S. Food and Drug Administration (FDA) as a surrogate for animal trials for preclinical testing of control
1. INTRODUCTION Diabetes mellitus, one of the most common metabolic diseases of human beings, is characterized by an incapability of controlling blood glucose (BG) concentration in the body. There are two basic types of diabetes mellitus: type 1 and type 2. Type 1 diabetes mellitus (T1DM) is caused by malfunction of the pancreatic islet β-cells to secrete insulin. Consequently, patients with T1DM, or so-called insulin-dependent diabetes mellitus (IDDM), must depend on daily insulin injections to regulate the blood glucose. These daily insulin injections artificially imitate the endogenous insulin secretion in healthy human bodies to maintain their BG levels within a normal glycemic range. This mimicry can be attained to a certain degree by two types of insulin delivery therapy. One is continuous subcutaneous insulin infusion (CSII) with an insulin pump, which provides a continuous basal insulin infusion rate and prandial insulin boluses. The other is multiple daily injections (MDI) with a syringe or an injector, which provides long-term effected insulin and prandial insulin boluses. In general, regardless of which insulin therapy is used, rapid-acting insulin is applied to prandial insulin boluses. However, making a decision about the optimal dosage for a bolus is still a challenge to most patients, especially when the patient has variety in daily diets and activities. Even though subjects consulted with physicians, the insulin sensitivity can change so that the dosage should be adjusted accordingly. It is impossible to consult with physicians every time before the subject decides on the amount of a bolus. Therefore, the objective of this work was to design and synthesize a human-like fuzzy-logic supervisor to provide adequate recommendations on bolus injection that can gradually be updated meal-by-meal. To date, quite a few works1−18 have contributed to improving CSII therapy, which incorporates a continuous glucose monitoring (CGM) device. With online measurements from the CGM device, automatic control algorithms, for example, model © 2013 American Chemical Society
Received: Revised: Accepted: Published: 1678
June 19, 2012 January 4, 2013 January 4, 2013 January 5, 2013 dx.doi.org/10.1021/ie301621u | Ind. Eng. Chem. Res. 2013, 52, 1678−1690
Industrial & Engineering Chemistry Research
Article
where Ibolus refers to the insulin bolus. CHO represents the meal carbohydrate intake. ICR is the insulin-to-carbohydrate ratio, which is a function of CHO. G0 is the glucose measurement at the onset of the meal. The index n refers to the current meal, and the index n − 1 refers to the previous meal. ISP is the insulin stacking percentage, which can be evaluated based on the interpolated insulin stacking percentage profile. An example of how to estimate ISP is shown later in experiment 3 of section 5. ISF is the insulin sensitivity factor. For simplification purposes, this sensitivity factor is calculated from the ICR using an 1800/500 ratio as follows
strategies in January 2008. By using this recently developed and well-acknowledged meal simulation model of the glucose−insulin system for T1DM, the simulation environment was established to synthesize and test the control strategy.6,8−10,14 In our previous article,14 two virtual subjects were employed, and an identified intermediate Hovorka−Wilinska (HW) model3,32 to replace the subjects for the development of a model predictive control (MPC) algorithm was also applied. A patient with CGM and under CSII therapy is required for the implementation of the MPC algorithm. In this article, a proposed fuzzy-logic supervisor is synthesized based on the identified HW model and then tested on two virtual subjects. A supervisor is developed that can be applied to either CSII or MDI therapy and also without the requirement of a patient with a CGM device. The contents of this article are arranged as follows: In section 2, our proposed control method is introduced. In section 3, based on the identified HW model, the preliminary optimal values of boluses for different meal sizes are obtained. Then, the empirical relation between the insulin-tocarbohydrate ratio (ICR) and carbohydrate (CHO) is built. In section 4, a fuzzy-logic controller is synthesized, and an online parameter adaption scheme is employed. In section 5, our proposed fuzzy-logic-based supervisor is employed for six experiments of preclinical testing on two virtual subjects. In section 6, validation based on two additional subjects is demonstrated, and comparisons to other methods and limitations of our proposed algorithm are discussed. Some concluding remarks for this study are made in section 7.
ISF =
G0 − 110 CHO(n) + ICR[CHO(n)] ISF[ICR(n)] − Ibolus(n − 1)ISP
(2)
where the 1800/500 ratio is a simple unit transformation factor based on the 1800 rule and the 500 rule,34 which are used in the clinical applications. It should be noted that ICR is the most important factor in determining the amount of a bolus in eq 1, and ICR is related to different meal sizes and affected by insulin sensitivity changes. To obtain an appropriate ICR for each meal, we designed a relation between ICR and CHO, which is detailed in section 3. The second term of the bolus dosage equation in eq 1 is the glucose state correction, which is used to compensate for the effect of a higher or lower glucose state. The last term of this bolus dosage is the insulin stacking correction, which is used to reduce the amount of dosage because of previous insulin stacking. The injection time of the insulin bolus is assumed to be at the onset of the meal. To overcome the problem of insulin sensitivity changes, we synthesized a fuzzy-logic controller to adjust the ICR meal-bymeal. This adjusted ICR is used to update the relation between the ICR and CHO for the calculation of the next meal. Our proposed fuzzy-logic controller is introduced in detail in section 4. The proposed supervisor can provide an appropriate value of ICR for the current meal based on the three-phase mechanisms. During the recall phase, the empirical relation between the ICR and CHO is used to obtain the ICR for the current meal. During the inference phase, a fuzzy-logic controller is used to adjust the recommendation of the ICR. During the learning phase, the adjusted ICR is used to update the relation between ICR and CHO. To make the supervisor work, only two measured glucose points are needed for each meal. One is G0, which is used to calculate the correction of the bolus dosage from the current glucose state, and the other is G3hr, which is an input variable to the fuzzy-logic controller. The block diagram of this supervisor is summarized in Figure 1.
2. OVERVIEW OF THE SUPERVISOR FOR INSULIN BOLUS DELIVERY To provide a more accurate and safer bolus dosage, a fuzzy-logicbased supervisor is proposed. This supervisor is aimed to give bolus dosage recommendations and can gradually be updated meal-by-meal. It consists of a three-phase algorithm, including recall, inference, and learning phases. Our goal is to mimic the mechanisms similar to the human thinking of a physician. The supervisor is planned to make decisions depending on the meal sizes and glucose profiles of the subjects and is expected to tackle control problems due to insulin sensitivity changes during a subject’s daily life. The dosage of an insulin bolus is calculated according to the equation33,34 Ibolus(n) =
1800 ICR 500
(1)
Figure 1. Block diagram of the fuzzy-logic-based supervisor. 1679
dx.doi.org/10.1021/ie301621u | Ind. Eng. Chem. Res. 2013, 52, 1678−1690
Industrial & Engineering Chemistry Research
Article
3. BOLUS OPTIMIZATION BASED ON THE HW MODEL To design a preliminary optimal preprandial bolus dosage for each meal intake, we conducted nonlinear optimization based on the intermediate HW model identified from a patient. Detailed descriptions of how to obtain the HW model from a three-day protocol of glucose measurements, meal contents, and injected insulin can be found in Liu et al.14 The objective function for finding the optimal preprandial bolus dosage using the HW model is given by
Table 1. Parameters of the Linear Models for the Two Subjects
a
parameter
virtual subject 1
virtual subject 2
p1 p2 ICRa CHOb
0.348 0.652 11.54 90
0.331 0.669 6.95 90
ICR* = ICR/ICR. bCHO* = CHO/CHO.
N
Ω= I
∑ {ηt [Gr − GM(t )]}2 t=1
injection of the corresponding insulin bolus can be applied, and the resulting glucose profiles can be summarized in statistical plots as shown in Figure 3.
(3)
where the integer N refers to the end of the simulation. In the case of our simulation, the simulation time was assumed to be one day (i.e., N = 288 with a sampling time of 5 min, not counting the initial point). The desired value of BG is Gr. In this work, Gr was fixed at 110 mg/dL. GM(t) represents the simulation outputs based on the HW model. The vector ηt consists of weights for zone penalty. The definitions of the six zones of BG proposed by Liu et al.14 were adapted as follows: In zone I, for 100 mg/dL
