Case Studies and Project Ideas: Diabetes Dynamics

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Overview:

Glucose is the major fuel used by the body to generate energy. Glucose is released into the bloodstream through digestion of food, or through the breakdown of fat in the liver. This particular model only looks at the breakdown of fat in the liver. Under normal conditions, roughly 4.5 grams of glucose are released each minute. Once in the bloodstream, glucose is transported to peripheral tissues. There, it is either taken up by cells and stored for later use, or burned.

Insulin is the primary substance that the body uses to regulate glucose levels in the bloodstream, whose volume (taken together with tissue space) is roughly 15 liters. High concentrations of insulin both encourage glucose uptake into cells, and depress its release by cells into the bloodstream. Insulin is secreted by beta cells within the pancreas. Insulin is a hypoglycemic (low blood sugar) peptide that is essential for the synthesis and conservation not only of carbohydrates, but also of fat and protein.

Figure 1: the pancreas, producer of insulin

Pancreas

Large Intestine

The rate of insulin secretion increases as the concentration of glucose within the bloodstream rises beyond its normal value of 150 mg/deciliter (dL). Under normal conditions, about 20 units of insulin are secreted each minute. Once released, insulin remains active for about 15 minutes before it degrades, losing its ability to influence glucose uptake and release.

The purpose of this model is to develop an understanding of how insulin regulates glucose levels in the bloodstream, and then to use this understanding to shed some light on different hypotheses concerning the cause of diabetes. You will want to simulate at least three types of patients:

1. Normal, non-diabetic person
2. Slightly diabetic patient
3. Severely diabetic patient

Building the Model:

Some suggestions for building this model:

Description of the Glucose Section:
Initial amount of glucose: 150 units

Glucose in the bloodstream increases two ways:

1. Normal release from the liver and from digestion of food (considered to be one process in this particular model). Normal release is defined by the normal release rate (4.5) times the impact of insulin on the release of glucose. The impact of insulin on release of glucose is defined graphically using the chart below:

   Insulin concentration	Impact of insulin
   0	1.60
   10	1.30
   20	1.00
   30	0.85
   40	0.73
   50	0.64
   60	0.57
   70	0.53
   80	0.48
   90	0.44
   100	0.41

2. A sudden infusion of glucose from an intravenous Glucose Tolerance Test (IVGTT). We will assume that 100 grams of glucose are going to be injected at some time. Initially, the IVGTT will be set to be administered at 300 minutes from the beginning of the simulation (meaning, that when the simulation is first run, no IVGTT will be administered). Once the simulation has been run WITHOUT the IVGTT, change the administration time to 5 minutes, not to be repeated. Use the PULSE command to do this:
   PULSE(volume, first pulse, interval)

So PULSE(10,20,30) would add 10 grams to the system at the 20 time mark, and then again at 50, 80 etc. It is a good idea to specify these three numbers as converters so that they can be easily manipulated!

Glucose is taken up in the bloodstream proportional to how much is in the bloodstream. Uptake is defined by the total amount of glucose times its uptake fraction. Uptake fraction is a function of the insulin concentration:

The last variable is glucose concentration. Glucose concentration is defined by the total amount of glucose divided by the total amount of tissue space. Units of concentration are milligrams per deciliter, or mg/dL.

Description of the Insulin Section:
Insulin is increased by secretion of insulin from beta cells in the pancreas, and degraded over time proportional to the amount that is in the system.

There are two types of insulin in this particular model: inactive insulin and active insulin. Active insulin is the only type of insulin that interacts with the glucose, and it is this type of insulin for which we will calculate the insulin concentration.

Inactive insulin accumulates by secretion from the pancreas. Secretion is defined by the number of beta cells times beta cell productivity. Each beta cell is assumed to have a certain productivity in secreting insulin. Beta cell productivity is defined as the base beta cell productivity times the effect on glucose on insulin productivity. The higher the glucose concentration, the higher the productivity of the beta cells in the production of insulin.

Glucose concentration	Effect of glucose on insulin productivity
0	0.00
5	0.46
10	1.00
15	1.46
20	1.98
25	2.34
30	2.72
35	3.02
40	3.26
45	3.42
50	3.48

One of the key factors that decides whether or not a patient is diabetic is the level of base beta cell productivity. For "normal" persons, base beta cell productivity is defined at 0.02, which, combined with the effect of glucose, determines how productive each beta cell is. For diabetic patients, the productivity fraction of these beta cells is less. You can simulate a diabetic patient in this manner:

Severely diabetic patient: Base beta cell productivity = 0.02 * 0.50 (50% or less if you desire)

In order to simulate a diabetic patient, you might want to experiment with a loss of productivity of the base beta cell productivity. You can use the STEP function to define base beta cell productivity as:

Base beta cell productivity = 0.020*(1-decrease in productivity)

Setting decrease in productivity at 0.25 will result in 25% reduction in the basal secretory capacity of beta cells. If you set the decrease at this level, the mathematics becomes:

Base beta cell productivity= 0.020*(1-0.25) = 0.020 * (0.75) = 0.015

To implement the test, change the decrease in productivity from its initial value of 0 to some percentage in decimal form. The effect of glucose on productivity is a function of glucose concentration (not total glucose), based on the chart below:

The initial amount of inactive insulin is a CALCULATED value, based on the algorithm below:

Initial amount of inactive insulin = number of beta cells * beta cell productivity * activation time

Active insulin is obtained through activation (change in) inactive insulin to active insulin, based on these mathematics:

Activation of inactive to active insulin = amount of inactive insulin / activation time

The activation time is typically around 15 minutes. Active insulin also decreases by a degradation process. This process is mathematically defined as:

Degradation of active insulin = amount of active insulin / degradation time

Degradation time is also set at 15 minutes.

The initial amount of active insulin is CALCULATED through these mathematics:

Initial active insulin = amount of inactive insulin* degradation time/activation time

Insulin concentration is defined the same as glucose concentration.

You should run this model for 200 minutes at a normal DT. The desired glucose concentration level is 150 mg/ dL, you might want to consider using a converter to hold this value and use it when you are looking at the graph. On the graph, you are interested in looking at the concentration of glucose level. Levels above 150 mg/dL become increasingly dangerous, especially if they reach the 300-400 mg/dL level. Levels below 30 mg/dL are typical of patients entering diabetic coma. You may want to have two converters, one called "Diabetic shock", with a value of 300 mg/dL, and one ÒDiabetic comaÓ, with a value of 30 mg/dL. Display these on your graph.

EXTENSION:

You might want to consider adding a way to inject active insulin into the patient if, during the running of the IV glucose tolerance test, the patient reaches particularly high levels of glucose concentration. Consider using the PULSE function to help you to do this!

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