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GLUCOSE AND INSULIN ON DIABETES DISEASE MODEL

Soesanto1

1Department of Informatics Techniques,STMIK Mikroskil, email :

Abstract

Mathematical model for glucose and insulin concentrations in the blood involves no simultaneous linear differential equations and includes several parameters. The model is derived from the oral glucose tolerance test mechanism that describes the behavior of the real system of the normal physiology and diabetes. Basic assumptions used in formulating the overall picture of the system of regulation of glucose and insulin in the blood is a simplification of a known interaction between glucose, insulin and other hormone regulation.

Keywords: models, glucose, insulin, regulatory system, hormone

  1. INTRODUCTION

In connection with the development of science is marked by the emergence of an increasingly complex discipline and discovery of things - new things in science, the science of mathematics as the container has historically emerged from the desire of humans on natural events in which he lives. Solving problems in the real world with the math done by converting the problem into mathematical language. Such a process is called as mathematical modeling or mathematical.(Baiduri, 2002)

The mathematical model is a business that outlines several things related to the world of reality into mathematical form, while a model is a representation of a thing or system we are studying, such as objects, events, or events, processes or systems and models can also be used as a tool to predict and control it. The main function of the model is to explain a thing, but not as a descriptive.

There are many different models on glucose-insulin regulatory system. The model has two equilibrium points are then analyzed stability of the equilibrium point to determine the dynamic behavior of the concentration of glucose and insulin, because both the point of balance is negative, then for subsequent analysis using the first equilibrium point and because the pattern of the first movement is the fastest and wear around only 10 seconds. The second motion patterns called rapid oscillation and wear about 5-15 minutes, and the last movement pattern called ultradian oscillation and wear 50-120 minutes (Suyono,2007).

  1. LITERATURE

Glucose

Glucose (blood sugar) is a monosaccharide with 6 carbon atoms (C6H12O6), which serves as the main unit forming carbohydrates. The main function of glucose in the human body is a trigger fuel.

Glucose is also an important carbohydrate used as a source of energy for living things, and one of the main results for the initial photosynthesis and respiration. Glucose is a hexose - a monosaccharide containing six carbon atoms with a molecular weight of 180.18, due to glucose-containing group - CHO, then Glucose is an aldehyde. Five carbon with oxygen to form a ring called a "pyranose ring". In this ring, each carbon bonded to the hydroxyl side groups and hydrogen atoms except the fifth, sixth carbon attached to the outside of the ring, forming a CH2OH group. This ring structure is in equilibrium with a more reactive form, the proportion of 0.0026% at pH.

Glucose can be formed from formaldehyde in the abiotic state, so it will be easily available to primitive biochemical systems. It is more important to the organism level up is the tendency of glucose, as compared to other hexose sugars, which are not easily react non-specifically with the amino group of a protein.

Glycosylation reactions reduce or even impair the function of many enzymes. The low rate of glycosylation is because glucose is mostly located in the less reactive cyclic isomer. Acute complications such as diabetes, blindness, kidney failure and peripheral nerve damage ("peripheral neuropathy"), probably due to protein.

Normal human blood glucose levels several hours after eating about 80 mg / 100 ml of blood, but shortly after a meal will be increased to 120 mg / 100 ml(Price & Wilson, 1995).

Insulin

Insulin is a hormone produced by cells - Lagerhans island β cells in the pancreas. Insulin is also the principal agent responsible for maintaining proper blood sugar levels. Sugar causes insulin to move into the cell so that it can produce energy or stored as energy reserves (Price & Wilson, 1995).

Increased blood sugar levels after eating or drinking stimulates the pancreas to produce insulin, thus preventing blood sugar levels rise further and cause blood sugar levels slowly decreased and at the time of physical activity in blood sugar levels can also be decreased because the muscle use glucose for energy.

The main function of insulin is to convert glucose into glycogen (muscle sugar) in the liver, so the hormone can lower glucose levels in the blood.

Glucose test levels in the blood

Blood glucose levels can be detected by under this tests:

  1. Blood glucose levels tests at any – time.
  2. Tests of fasting blood glucose levels.
  3. Tests of blood glucose levels following administration of a glucose dose.

There are 2 types of tests, namely :

  1. 2-hour Postprandial Blood GlucoseTest

2-hour postprandial blood glucose test is a test to determine a person's ability to throw a dose (load) of existing glucose.

This test consists of a patient's blood glucose levels 2 hours after eating 75 grams of glucose orally.

  1. Oral Glucose Tolerance Test

This test will be performed if the 2-hour postprandial glucose test is abnormal and this test also can provides a more complete description of the disorder of carbohydrate metabolism

In this test, normal fasting glucose levels were measured, then the patient will be given a meal as much as 75 grams of glucose within 5 minutes. Blood glucose levels were then measured in half-hour intervals for 2 hours after glucose administration.

Fasting blood glucose levels normal person is 80-115 mg / 100 ml. Blood glucose levels after glucose administration will initially increase, then will return to normal levels within 2 hours.

The value for the normal oral glucose tolerance test is defined:

  1. Blood glucose less than 200 mg / 100 ml at minute 30, 60 and 90
  2. Blood glucose less than 140 mg / 100 ml at minute 120 (National Diabetes Data Group Criteria)(Ilyas,2009)

Basic - basic mathematics

Establishment of a mathematical model of a problem can use a variety of methods. Mathematical models are used to seeing dynamic behavior, usually using differential equations.

2.1.1Differential Equations

Definition 2.1

Differential equation is an equation that contains one or more derivatives dependent variable to one or more variables are not dependent (Swindle, 2007).

Initial value problem of differential equations is to obtain the solution of differential equations ϕwhich is defined in the real interval containing x0and satisfy the initial condition ϕ(x0) = y0or can be written :

(1)

2.1.2Not Linear System

View of differential equations :

(2)

This equation will be equivalent to a system of two equations.

(3)

The solution of (2) consists functionsof (x1 (t), x2 (t)), t Є I ⊆ R, which satisfies the equation (3)(Dahlan, 2008).

  1. MAIN RESULTS

Preview Blood Sugar Levels

Based on the research results obtained, the results of pre-test mean of 157.40 mg / dLso get into the control of blood sugar, then after doing gymnastics diabetes the average post-test score be 117.80 mg / dLand enter into good blood sugar control. So from the pre-test and post-test changes in the value of the average obtained by 39.60 mg / dL

According PERKENI (2006) the value of good blood sugar control if the average blood glucose 80-144 mg / dL, moderate if 145-179 mg / dL, bad if >= 180 mg / dl.It is the same as the theory proposed by Santoso (2008), that changes in blood sugar is due at the time of exercise (gymnastics), energy needs will increase so that the muscle becomes active and more sensitive and makes insulin receptors become more active resulting in increased glucose utilization which led to a decline in blood sugar levels and sugar darahpun results changed, and it is also motivated by factors of continuity or regularity of diabetic patients in the follow gymnastics. This is because that the exercise diabetes can also control blood sugar, especially in type II diabetes mellitus who follow the sport on a regular basis, due to the exercise of diabetes, the blood glucose will be burning the change of blood glucose into energy and energy cells become more sensitive to insulin.

Univariate discussion

3.1.1 Age

Age is the period of life from birth to death, the age calculation is calculated in units of years. Age of the respondents were divided into two categories, namely, age 45-60 years and age> 60 years, and based on the above study, showed that of the 20 respondents who observed there were 9 respondents (45%) aged 45-60 years and 11 respondents (55 %) aged> 60 years.

3.1.2 Sex

Sex is the biological markers that distinguish human beings into two groups (Marhijanto, 2005).Based on the research above, shows that of the 20 respondents there were 11 respondents were female (55%) and 9-sex male respondents (45%). The results showed that more female respondents than male respondents. This is because the proportion of diabetes that follows exercise more women than men, and the research time more female respondents who were respondents in the study. It is also consistent with the theory proposed by Brunner & Suddart (2002) which states that more female patients suffering from diabetes mellitus than male patients (Dahlan, 2008).

  1. CONCLUSIONS

In this research, my conclusion from the discussion of the analysis of mathematical models of glucose and insulin concentrations in the blood are as follows :

  1. Dynamics of glucose and insulin concentrations in the blood of normal individuals differ with diabetes. In normal people, high blood glucose concentrations may be offset by high concentrations of insulin as well. So that normal blood glucose levels can still be maintained properly. So for people with diabetes, high blood glucose concentration can not be offset by high concentrations of insulin also. So that the blood glucose levels in diabetics is always high and exceeds normal levels.
  1. Concentration of glucose in the normal more quickly reach maximum levels than diabetics. That's because normal people that the body's ability to absorb glucose is still high compared with diabetics.
  1. Mathematical model for glucose and insulin concentrations or significant enough fit is used to determine the dynamics of glucose and insulin concentrations in the blood of normal individuals or in patients with diabetes. So that the model can be used enough to represent a depiction of the changing dynamics of glucose and insulin concentrations in the blood in general.

REFERENCES

Baiduri.(2002). Differential Equations and Mathematical Models. Malang: UniversitasMuhammadiyyah Malang Press.

Dahlan, M Sopiyudin. (2008). For Medical and Health Statistics. Jakarta: SalembaMedika.

Ilyas, Ermita. (2009). Integrated Management of Diabetes Mellitus.Jakarta : FKUI.

Marhijanto, Drs. Bambang. (2005). Popular Indonesian dictionary.Surabaya :BintangPelajar.

Price, S. A., Wilson, L. M. (1995). Pathophysiology Clinical Concepts of Disease

Processes. Jakarta: EGC.

Suyono, Slamet. (2007). Textbook of Internal Medicine 4th Edition Volume III.Jakarta : FKUI.

Swindle, M.M. (2007). Swine in the Laboratory: Surgery, Anesthesia, Imaging, and Experimental Techniques.CRC Press, Taylor & Francis Group.