System Insulin Pancreas
Blood Glucose-Insulin Regulation and Management System Using MATLAB/SIMULINK
Abstract-The main purpose of this study is to regulate the production of insulin by the Pancreas. One of the main functions of the pancreas is to regulate glucose concentration in the blood through the release of the enzyme insulin. Some theoretical analysis of the control of blood glucose levels in diabetic individuals is undertaken using a simple mathematical model of the dynamics of glucose and insulin interaction in the blood system developed by Stolwijk and Hardy dynamic model. The model was modified by adding a term for exogenous insulin infusion. Using this model we simulate blood glucose and insulin regulation levels in the body through closed loop feedback controls. The simulation is done using powerful engineering software MATLAB/SIMULINK. This closed loop system will act as an artificial pancreas on day-to-day basis.
Keywords-insulin; pancreas; closed loop feedback controls; simulation; MATLAB/SIMULINK
- INTRODUCTION
Diabetes Mellitus is an incurable disease affecting million of people worldwide. It can damage to the systems that can lead to pathological changes with eye, kidney, nerve, heart and vein. Approximately 177 million people have diabetes, and this number is expected to increase to 300 million by the year 2025 [1].Scientists are focusing on developing a manifold of new techniques and feasible instrumentation to offer wearable solutions and improve the life of patients. The patient is totally dependent on an external source of insulin to be infused at an appropriate rate to maintain blood glucose level. The blood glucose level should be controlled within the range of 60-120mg/dl. [1].
The current medical treatments suggest three to four daily glucose measurements and an equivalent amount of subcutaneous insulin injections. This method is not only inconvenient and painful but also unreliable due to the approximation involved in the amount and type of insulin delivered. Fortunately, a significant amount of research is being carried out to overcome the shortcomings of the current medical practice and is discussed in the following paragraphs. The main research issues that are being investigated are concerned with: the site and the mode of insulin delivery [1].
Hyperglycemia is common in critically ill patients and is not limited to patients who are known to be diabetic. Several recent studies have established a correlation between tight glucose control and decreased preoperative morbidity and mortality in surgical and critically ill patients. Applying these findings to improve outcomes involves identifying patients at risk for hyperglycemia, monitoring blood glucose frequently, using an effective insulin infusion algorithm to control blood glucose within a narrow range, and adjusting insulin infusion rates in a timely and accurate manner. Adverse effects of hyperglycemia include dehydration, increased susceptibility to infection, and impaired wound healing. In fact, there are some data to suggest that aggressive glycemic management can help combat infection and several studies have showed a strong association between hospital mortality and glycemic levels. Whether the survival benefit is due to glycemic control or to insulin administration is still unresolved. The survival benefit of intensive insulin therapy is likely multifactorial and regardless of the mechanism, optimizing glycemic control with insulin infusions clearly appears to be beneficial [2].
A number of algorithms for controlling glucose levels with insulin infusions are currently in use throughout the world. Most of these protocols specify adjustments in insulin infusion rates based on hourly measurements of blood glucose with rescue administration of glucose for hypoglycemic episodes. The development of insulin injection programs has generally proceeded along two fronts: open-loop method and closed-loop method [3].
- Open Loop Method
Open-loop programs deliver a predetermined amount of insulin to the patient and the amount of insulin is based on the insulin curve of the normal pancreas secretion. Open-loop control block diagram shows in Fig.1.
- Closed Loop Method
In the closed-loop control system, it need use a glucose sensor that can measure blood glucose level. This information then would be passed to a control system that would calculate the necessary insulin delivery rate to keep the blood glucose level in a stable range. Then a mechanical pump can deliver the desired amount of insulin. In general, the closed-loop method is more reliable in maintaining the level of blood glucose and also is close to the normal pancreas [4]. Fig.2 shows the block diagram of closed-loop control of diabetic patients.
For patients with diabetes especially for type 1 insulin-dependent diabetes, tight control of glucose level is essential. Regulating blood glucose concentration using the insulin infusion pumps is important for these patients, because they have deficiency of insulin production by pancreas that prevents appropriate metabolism of glucose. Many patients, who take insulin infusion in their diabetes therapy, inject insulin with needles and syringes that deliver insulin just under the skin, so that the functions of the pancreas are replaced by some external devices. An external insulin pump is an electronic medical Device that delivers insulin through narrow and flexible plastic tubing that ends with a needle inserted just under the skin near the abdomen. The pump releases doses of insulin at meals and during the periods when blood glucose is too high based on measured values of glucose sensors [5]. A patient's glucose concentration may change dynamically depending mostly on his/her physical activities and nutrition, and therefore, the amount of insulin needed varies from time to time.. But to date, the current method of therapy is a series of 3~5 daily insulin injections with quantities of insulin based on 4~8 daily invasive glucose measurements. It is said that infusion of insulin is discretely controlled by users based on the feedback of several blood glucose measurements. It is obvious that such treatment is lack of a reliable continuous monitoring, which may make glucose concentration out of permitted range because of control delay. In other words, this kind of therapy cannot restore metabolism to a state of a healthy patient, and wide glucose fluctuations continue to occur on many patients. Therefore, it is urgent to design a continuous closed-loop control system for insulin infusion. The continuous control would be a great improvement in the daily treatment of diabetes, especially in some cases that medical persons are not presented or the patients have less knowledge about the disease. Such an automatic control will benefit patients and avoid some mistakes during injections and operations. [5]
II. GLUCOSE-INSULIN REGULATION MODEL
In order to study the effects of glucose and insulin regulation in the body we need a model of a pancreatic function. One of the main functions of the pancreas is to regulate the glucose regulation in the blood through the release of the enzyme insulin. In a normal patient, insulin tightly regulates the metabolism of glucose. Diabetic patients suffer from a dysfunction of this process. The glucose-insulin regulation model used is based on Stolwijk and Hardy's dynamic model. The model was modified by adding a term for exogenous insulin infusion. Hence, the glucose dynamics are governed by
CG= UG + QG-λ G - νGI, G≤ θ (1)
CG = UG + QG-λ G - νGI - µ (G - θ), G> θ,
Insulin dynamics governed in the body following equation
CI = UI - α I G≤ φ (2)
CI = UI - α I + β (G- φ) G> φ
Where,
G(t): Instantaneous blood glucose level in mg/dl
I(t): Instantaneous blood insulin level mU/d
UG(t): Exogenous glucose infusion in mg/h
UI(t): Exogenous insulin infusion in mU/h
CG: Glucose capacitance in the extra cellular space
CI: Insulin capacitance in the extra cellular space
QG(t): Glucose inflow into blood in mg/h
λ: Tissue usage rate of glucose that is independent of I(t)
ν: Tissue usage rate of glucose that is dependent on I(t)
α: Insulin destruction rate
β: Insulin production rate by the pancreas
θ: Threshold for renal discharge of glucose
φ: Threshold for pancreatic production of insulin
µ: constant proportionality factor (gain)
Glucose inflow into the blood can be either through absorption from the gastrointestinal tract or through production from the liver. In addition, as seen from the parameter descriptions above, the coefficients have physiological significance, and also differ depending on the condition of the patient. Type 1 Diabetic Mellitus (DM) patients lack the capacity to produce adequate amounts of insulin, The glucose-insulation regulation model, which is described in equations (1) and (2) and comprises an internal feedback loop provided by the pancreas, can be thought of as a two-input two-output dynamic system as shown in Fig.3
III. PARAMETER FOR GLUCOSE-INSULIN MODEL
The pancreatic model according to the dynamic equations (1) and (2) can be implemented in MATLAB/SIMULINK by the following parameters Stolwijk and Hardy are stated below. Plasma volume and interstitial fluid volume are represented in a single compartment (3L+12L, in the normal adult) with constant volume). The steady state concentration of glucose in this compartment is x (in mg/mL). Glucose enters through absorption from the Glucose-Insulin tract or through production from the liver at the flow rate of Q(G)t in (mg/h). Glucose leaves the extracellular volume to enter the cells to be metabolized and/or stored. In insulin independent tissue the rate of glucose utilization depends only on the extracellular to intracellular glucose gradient. The intracellular concentration is ignored Glucose uptake in insulin dependent tissue is facilitated by insulin concentration (y). Therefore, the rate of insulin dependent glucose utilization (UI (t)) is given as
UI (t) = νy
Insulin is produced at a rate dependent on plasma glucose levels. However if x falls below a certain threshold insulin secretion ceases. Insulin is removed from the plasma involving the insulinase enzyme at a rate proportional to its concentration in blood. The steady state concentration for insulin (y) is given as
Y= 0 , X= φ
Y= α (X- φ) , X> φ
Aside from the threshold nonlinearity, the insulin response to glucose is basically linear. The steady state level of glucose and insulin in the blood under a given set of conditions can be predicted from solving these equations simultaneously. The following parameter values are used for pancreatic model
Table 1
Parameters |
values |
G(t) |
2.5 mg/mL |
µ |
7200 mL/h |
λ |
2470 mL/h |
ν |
139000 l/(mUh) |
φ |
0.51mg/mL |
β |
1430mUmL/(mgh) |
α |
7600mL/h |
QG(t) |
8400mg/h |
According to the above parameters we implemented the glucose-insulin regulation model in MATLAB/SIMULINK. We choose different blocks which are performing the parametric action in the model as shown in the SIMULINK model in Fig 4.
IV. SIMULATION RESULTS
MATLAB is used to simulate the pancreatic model by using the parameters stated in the Table 1. The simulation results of the pancreatic model are show in Fig 5 and Fig 6.
From the above simulated model we show how a natural pancreas model can be implemented as artificial pancreatic model using SIMULINK. We conclude that the as the blood glucose in the blood become unstable the pancreas secretes insulin to regulate and control the blood glucose to its stable and control point. We see that as the blood glucose concentration x approaches to its peak value the pancreas secretes insulin with respect to the blood glucose level and when blood glucose is at its peak level the insulin concentration secretes by pancreas is also at its peak level which show a proportional relation between glucose and insulin in the body. As the blood glucose level approaches to stability or controllable state the pancreas secretion becomes slow till the end of stable blood glucose level in the body.
V. CONCLUSIONS
From the above discussion and results we conclude that the model in not a perfect model. There are many reasons. One of the main reasons is that in the closed loop control systems the main part is the sensor which has to be more efficient and should detect the disturbance in at the output of the feedback control system. Currently, the clinical application of the blood glucose control is mostly using open-loop method, so how to improve the mathematical model of insulin curve, which is worthy discussing. So do some researches about finding the rules of human insulin secretion will be a very significant project. The closed-loop method is a new direction, and it can control human blood glucose ideally. At present, using of appropriate control algorithm to regulate blood glucose is becoming a new direction for the treatment of diabetics. Apart from the controller, there are still some technical problems. The first is the glucose sensor, because closed-loop control needs an accurate blood glucose signal. How to measure the blood glucose concentration stably and reliably is an important problem. The second is the biological compatibility problem. Both the mechanical pump and the blood glucose sensor are necessary to consider the compatibility of the human body. Now the closed-loop control method has been mentioned more and more, but it has not applied widely. To obtain the excellent control methods of blood glucose level, we should make great efforts on it.
VI. REFERENCES
[1] Pinky Dua, Francis J .Doyle, and Pistikopoulos, “Model-Based Blood Glucose Control for Type 1 Diabetes via Parametric Programming,” IEEE Transactions on Biomedical Engineering, vol.53, pp.1478-1491, August 2006
[2] Nicolas W. Chbat, Tuhin K. Roy “Glycemic Control in Critically Ill Patients - Effect of Delay in Insulin Administration” Proceedings of the 2005 IEEE Engineering in Medicine and Biology 27th Annual Conference Shanghai, China, September 1-4, 2005
[3] [3] Zlatko Trajanoski, Paul Wach, “Neural Predictive Controller for Insulin Delivery Using the Subcutaneous Route,”IEEE Transactions on Biomedical Engineering, vol.45, pp: 1122-1134, 1998
[4 ] J.Geoffrey Chase,Z-H Lan,J-Y Lee,and K-S Hwang, “Active Insulin Infusion Control of the Blood Glucose Derivative,” Seventh International Conference on Cootrol, Automation, pp.1162-1167,December 2002
[5] Jiming Chen, Kejie Cao,1 You Xian Sun, Yang Xiao, and Xu (Kevin) Su, “Continuous Drug Infusion for Diabetes Therapy: A Closed-Loop Control System Design” Received 15 July 2007; Revised 25 November 2007; Accepted 5 December 2007
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