Fuzzy System-based Modelling of the Biological Regulator of Glycemia

Diabetes mellitus, illness related to a deficient regulation of glycemia, can cause serious complications in patients’ health. Several artificial mechanisms for controlling glycemia exist, which try to replace the biological system. However, these mechanisms do not generally achieve an optimal control. We propose a specification of the biological glycemia regulation system, bearing in mind the knowledge given by experts and obtained from bibliography, and a regulating mechanism that complements to the biological system. For the design of the regulator, based on the control of glucose and insulin in blood, we propose a control system made up of different modules, where each one of them is put in charge of some type of substances that play a role in the glycemic control, and they are designed using fuzzy control structures. A collection of experiments has been carried out by means of a simulation of the proposed model, checking that fuzzy control provides good results for the studied cases. 1 Problem Exposition 1.1 Biological Problem Glucose is an essential substance for cellular nutrition, especially for the muscular tissue and the brain, and its normal concentration (from a clinical point of view) is within the range of 70-120 mg/dl of blood. Hyperglycemia (high glucose level) as well as hypoglycemia (low glucose level) are dangerous for patients’ health (glycemic coma, blindness, etc) [1, 2]. Pancreas is an organ that perhaps carries out the most important function related to the biological regulating mechanism of glycemia; the so-called hormone insulin (segregated by the pancreas) is the main regulator of the glycemic levels. On the other hand, when there is a hipoglycemic condition, another hormone called glucagon is produced, which stimulates the glycogenolysis or glucose release from the hepatic reserve. Insulin reduces glucose concentration in blood, facilitating the glucose absorption by target cells (muscular, cerebral, hepatic, etc.). A full or partial failure in insulin secretion causes the illness known as diabetes mellitus. Other hormones influence on this regulating mechanism, such as adrenaline, but they have less incidence on it compared with insulin and glucagon. Moreover, other subsystems take part in this mechanism, such as the renal filter which eliminates the glucose excess in blood through the urine, when glycemia exceeds certain threshold. 1.2 The Problem of the Artificial Regulation Most research in the field of diabetes is devoted to achieve an optimal metabolic control, by using artificial mechanisms of regulation that substitute or complement to biological regulating system. The most usual artificial mechanism to regulate glycemia consists on the injection of several daily doses of synthetic insulin [2]. This therapy does not achieve a good control of glycemic level, because it is difficult to adapt the necessities of insulin throughout the day with punctual external supplies of it. Frequently, hypoglycemic episodes can appear in the very next hours to each injection, whereas the glucose level can be high lapsed several hours. In order to adapt the insulin supply to the individual’s necessities along the day and, therefore, to simulate more accurately the biological mechanism of glycemia regulation, a device called insulin pump has been designed [3, 4]. This device consists of an insulin reservoir, a catheter and a remote control system, in charge of giving the insulin quantities that have been previously programmed. Results of this therapy are quite positive, since the episodes of severe hypoglycemia practically disappear and the blood parameters are closer to normal values. However, some inconveniences associated to this treatment exist, like the risk that bears the surgical intervention for the subcutaneous installation of the device, and the feedback lack in the insulin infusion related to the glucose level. The necessity of a previous programming which implies a lack of autonomy in its functionality, leads to reflect on the possibility of designing an intelligent device that, according to the different detected glucose levels, was able to provoke the necessary actions to achieve a normoglycemic level. 2. Regulation Systems In order to model the biological system we are studying, we have to consider how much each model fits the system features. The classic regulation models (PID type) have been widely studied and contrasted for being applied to linear systems or, in general, systems that are highly structured [5]. However, the dynamics of the system we deal with are not accurately known, which implies that the behaviour of a PID regulator and the derived results of its application could not be quite appropriate. Models based on neural nets or genetic algorithms have the advantage of being able to be applied to poorly structured systems, from whom a knowledge base of relevant dimension is not a priori possessed. As a counterpart, we can point out the necessity to collect a wide set of empiric data which allows to infer regulation mechanisms based on the typical learning algorithms of these models [6]. Regulation models based on fuzzy sets are mainly applied to systems that have a knowledge base that could be virtually equal to the one a specialist has, where decisions are made depending on the combination of values of certain factors [6, 7, 8]. This would be the case of the system we are studying, so we will try to apply the fuzzy regulator features regulators to the problem of glycemia regulation. It is necessary to bear in mind that, in most cases, fuzzy models are complemented with neural or genetic methods which allow to modify the system of inference rules or other significant aspects as results are more and more accurately being obtained [9, 10]. 3. Basic Problem Specification Oriented to its Fuzzy Design In order to model this biological system, we will base on the following components: • Pancreatic insulin provider subsystem (glucose elimination) • Pancreatic glucagon provider subsystem (stored glucose release) As explained before, one can find some other components or subsystems which participate in the glycemia regulation; however, they don’t appear in this model because we consider that they would be a part of an external subsystem to the pancreas and that, in normal situations, their incidence in the regulation system is minimum [11, 12]. In table 1 glucose levels are divided into groups, determining different states: Table 1. Glucose levels associated to the different metabolic states (L=low; M=medium; S=severe; VS=very severe) Metabolic state Normoglycemia Hypoglycemia Hyperglycemia Degree L M S VS L M S VS Glucose (mg/dl) 70–110 65-70 60-65 50-60 < 50 120-140 140-250 250-300 > 300 It is necessary to keep in mind that the relationship between the amount of segregated insulin and glucose concentration in blood is not accurately known, although the function which relates both factors is considered to adopt the form of a sigmoid curve [1], just as shown in figure 1. 0 20 40 60 80 100 120 140 0 100 200 300 400 500 Blood Glucose(mg/dl) P la sm a in su lin ( m U /l) Fig. 1. Curve that relates the secreted insulin to the glucose concentration We can observe that a basal secretion of insulin exists (that is, a minimum amount whatever the metabolic conditions are) and that it is around 25 miliunits per litre (mU/l). For glucagon secretion, as it is an opposite insulin hormone, that is to say, it counteracts insulin action, it is frequent to relate both hormones [1, 13]. The function that would provide glucagon secretion, taking the secreted insulin as a parameter, would correspond to the curve shown in figure 2. 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 20 30 40 50 60 70 80 90 100 110 120 Insulin (mU/l) G lu ca go n (m g) Fig. 2. Relation between secreted insulin and produced glucagon Lastly, the relation between the amount of insulin and the metabolised glucose is considered to be expressed by means of a curve similar to that one shown in figure 3. 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 20 30 40 50 60 70 80 90 100 110 120 Insulin (mU/l) C on su m ed g lu co se (m g/ kg /m in ) Fig. 3. Relation between secreted insulin and metabolised glucose