Simulated Blood Glucose Chemistry Analysis
for High School Students
Using Small-Scale Chemistry Techniques
and Engineering Design Aspects
with Flow and Reaction

Heather Kucklick
University High School
11550 Lokanotosa Drive
Orlando, Florida 32819
Summer 1998

Dr. Bernard Van Wie, Instructor
Dan M. Leatzow, M.S.
Chemical Engineering
Washington State University
Pullman, Washington 99164-2710

Introduction

Science

Glucose.  Carbohydrates abound in nature.  The simplest carbohydrate molecules are simple sugars known as monosaccharides.  Glucose and fructose are examples of these sugars.  They are structural isomers of each other.  Glucose is abundant in plants and animals.  Depending on its source it may be known as corn sugar, grape sugar, and blood sugar.  Fructose is found in honey and fruits.  When two sugars are condensed they form a disaccharide, such as sucrose.  Sucrose is commonly found in sugar cane and sugar beets of which the world produces more than 7 x 10⁹ metric tons per year.  When three or more simple sugars condense they form polysaccharides.  Starch, glycogen, and cellulose are examples of polymers of glucose monomers.  Starch and glycogen are forms of storage in plants and animals, respectively.  Cellulose can only be digested by a few microorganisms and therefore, is an important structural polysaccharide.

Glucose and humans.  In humans, glucose is a major energy source for all of our cells.  The hormonal control system of glucose is therefore very important.  The slightest variation of glucose in the bloodstream can cause serious problems.  If there is an increase in blood serum glucose the area of the pancreas called the Islet of Langerhans will produce beta cells that increase insulin production.  If there is a decrease in the glucose level, alpha cells are increased which causes the breakdown of glycogen to glucose.

If a person is hyperglycemic they produce too much glucose (>300 mg/dL), and suffer from a disease called diabetes.  Diabetes affects approximately 10 million Americans.  Ten percent of those have Type 1, insulin dependent diabetes mellitus, which consists of the lack of beta cells to produce insulin.  Most of the people with this type are diagnosed before the age of 40 with a peak at the age of 14.  Persons with Type 2, non-insulin dependent diabetes mellitus, produce insulin, however, their cells do not recognize it.  If untreated, diabetes may lead to retinopath with blindness, kidney failure, nerve damage, circulatory problems leading to amputation of feet or toes, heart disease and/or stroke and ultimately death.  Because of the lack of insulin, the body does not absorb glucose, which then passes through the kidneys and increases the loss of fluids.  Most diabetics can lead a normal life by monitoring their blood sugars, taking insulin or other drugs, and exercising.  While diabetes results from an excess of glucose the antithesis is hypoglycemia, a lack of glucose (<50 mg/dL).  A hypoglycemic may experience weakness, shakiness, sweating, nausea, and a rapid pulse.

Testing for glucose.  One way of finding out how much glucose is in a sample is to use enzymatic reactions for detection of molecules.  A common system used clinically is the Trinder’s reaction.  This reaction employs glucose oxidase to oxidize glucose to D-gluconate and hydrogen peroxide.  The hydrogen peroxide in the presence of peroxidase, 4-aminoantipyrine, and p-hydroxybenzene sulfonate react to form a bright red dye, quinoneimine dye, which can be measured quantitatively.  The reaction sequence is shown below:

The degree of color change is proportional to the concentration of glucose.  Hospitals and laboratories are looking for faster, cheaper ways to perform this and other blood chemistries.  One possible way to do this is with a flow injection analysis system being developed by Professor Van Wie and research students at Washington State University and industrial collaborators.  Initially, this instrument is intended for rapid, automatic, and simultaneous analysis of the eight most common blood tests.  It involves injecting a small sample into a channel loaded with reagents.  The reaction occurs as fluid flows along the tube prior to being analyzed photometrically.  An important aspect of this system is that a smaller quantity of sample is needed; this reduces the waste produced.  In addition, the reaction is read before an endpoint is reached.  This allows tests to be completed in a one to three minute time frame.

Engineering

Laminar and turbulent flow.  Fluid flow in pipes can be defined as being either laminar or turbulent the difference being the behavior of the fluid as it moves through a pipe or channel.  A laminar flow has a uniform, parallel, velocity profile whereas; turbulent flow is non-parallel, non-uniform flow. Figure 1 shows an example of a laminar flow profile in a pipe.  Flow profiles of aerodynamic objects such as aircraft wings and cars are very often studied using wind or water tunnels, which use laminar flow patterns.

When thorough mixing is required, such as in home air conditioning systems, turbulent flow is required.  If the air came into the room in laminar flow the rooms would not cool off completely. A schematic representing turbulent flow is shown in figure 2.   Turbulent flow is far more common and useful than laminar flow.  This is due to the necessity of thorough mixing of fluids, either gaseous or liquid.

A convenient way to check for turbulence or laminar flow is by using the Reynold’s number, N_Re, as follows:

Where r, D, g, z, DL, and m represent fluid density, diameter, gravity, change in height, total length of the system, and fluid viscosity.  The parameters r, D, z, DL, and m are those that impact the Reynold’s number.  If the Reynold’s number is below 2100, laminar flow results.  Such a flow is characterized by fluid layers all traveling in the same direction, but each layer may have a different velocity.  Mixing between layers does occur as molecules diffuse from one layer to the next, but it is a very slow process. If the N_Re is well above 2100, turbulence and mixing occur. Roughness or bubbles inside of a pipe are other factors that change the N_Re by increasing the friction of the tube or altering the path of the fluid.

Teacher Prep

Glucose Reactions. Small-scale chemistry is used in my classroom and is congruent with the principles of Edward Watermen’s program. In the words of Edward Watermen, from Rocky Mountain High School in Fort Collins, Colorado, creator and author of Small-scale Chemistry (published by Addison-Wesley):

Small-scale chemistry is designed to put the learning of chemistry into the hands of students.  Students learn to do real experiments rather than just follow recipes.  Students participate in creative problem solving, invention, analytical thinking, effective writing, and descriptive chemistry while following the content of a standard high school chemistry curriculum.

Small-scale chemistry is designed to create a laboratory-based instructional chemistry program that fosters student creativity, invention, and problem solving.  Small-scale was not developed simply to do better what traditional laboratory experiments try to do.  Small-scale does not, for example, miniaturize traditional experiments.

Small-scale chemistry employs inexpensive, and for the most part, locally available plastic equipment, such as soda straws, cups, disposable pipets, and file protector sheets, to carry out suprisingly sophisticated and diverse experiments on hydrophobic plastic surfaces.  Students also build, calibrate, and use quantitative instruments, such as balances, digital burets, spectroscopes, and pH meters.  (page T4)

In the laboratory, the idea was to determine a qualitative analysis for glucose.  In order to accomplish this, a quantitative test was run on a MultiStat III+ clinical analyzer and Beer’s Law graphed.  After determining the linear range of the reaction, which is from 0 to 400, see Appendix E, concentrations that were relatively easy to discriminate were needed.  During the initial testing, the ratios obtained from the MultiStat III+ experiment were used.  A downfall to that procedure was that the ratio of glucose to reagent created a possible error, too many drops to count.  Various dilutions of glucose were tried and the at higher the concentrations of glucose, a constant consistent end point was reached, which meant that the glucose reagent became limiting.  It was determined that the solubility of oxygen at 30°C is 36 mg/dL.  Therefore, the final concentration, after addition of reagent, of glucose based on the chemistry of the reaction was calculated to be 2 mM.  From experimentation, the optimal glucose reagent was 2.5 mM.  Dilutions were then made from the stock solution as per the student’s experimental page.  The preparation of glucose reagent was made per the directions from the manufacturer provided in the kit.  Unknown samples for the students can be made by the teacher’s discretion so that the students need only add reagent to the sample.

Where to buy or call about donation of glucose reagent.

Reagent Applications, Inc.
1 - 800 - 438 - 6100

Sigma
1 - 800 - 521 - 8956

Laminar and turbulent flow.  The equations necessary for determination of the type of flow are found in Appendix B, C, and D.  An understanding of the derivations is not necessary for the use of the equations, but are provided as a reference for those who may wonder where the equations come from.  A diagram of a possible set up of the fluid flow system is seen below in figure 3.  The bottles were attached to the hoses by melting a small hole in a one or two liter bottle and quickly inserting the hose.  As long as the fit between the hose and the bottle is leak-proof the connection does not have to be rigid.  In the set up shown, three-one meter lengths of 7/16" (internal diameter) hoses were used with short pieces of 3/8" hose used as connectors.  The bottles were filled with blue and yellow dyed water.  This color scheme seemed to work best because the intermediate color of green was easy to visualize at dilute concentrations.  With this particular setup, the maximum height before the limit of laminar flow is reached was a difference of 5 cm.  The change in height is taken as the distance from the top of the water in the bottles to the end of the hose in the drain.  Other than density, diameter, viscosity, height, and length, factors that influence flow are rough joints from the connectors and bubbles in the line.  Using a refrigerated solution or boiling the water and cooling it in a sealed container are two ways of decreasing the bubbles.   Laminar flow is obtained when the two fluids come together at the Y-connector and travel down the tube with yellow on one side and blue on the other.  After the fluids come together at the Y-connector, diffusion of the two fluids to form a green boundary may be seen if the distance traveled is too long.

Two laboratories and one reflective experience follow.  The Glucose Laboratory Activity is designed to illustrate the quantitative components of what is normally a qualitative laboratory.  To conduct the laboratory entirely would take about 90 minutes, not including teacher preparation time.  The Laminar and Turbulent Flow Laboratory is designed to test quantitatively the flow mechanisms previously discussed.  This experience would require about 90 minutes.  The Real Life Applications section is designed to test student achievement of the module at the higher thinking level.

Glucose Laboratory Activity

Objectives:

• The student should be able to calculate the molarity of the stock solution given the mg/dL.
• The student should be able to calculate the dilutions required to make given concentrations.
• The student should be able to make the prescribed serial dilutions.
• The student should be able to determine the volume of the drops delivered and understand the implications of different drop sizes.
• Given unknown concentrations, the student should be able to find the appropriate range of the sample.
• The student should be able to understand the differences between qualitative and quantitative tests and understand when each is appropriate.
• Given quantitative data, the student should be able to plot Beer’s law and then use the graph to determine the concentration of a sample given the absorbency.

Materials supplied:

2.5 mM glucose solution
Glucose reagent

per student (or group)

1 - 1x10 well strip or equivalent
4 - labeled pipets (glucose, glucose reagent, water, and one for blowing air to mix the solutions)
1 - reaction sheet
2-3 - unknown concentrations of glucose

1. The initial stock solution was prepared by dissolving 1000 mg glucose/dL.  Given the formula of glucose is C₆H₁₂O₆, what is its molar mass?  ____________  What is the molarity of the initial stock sample of glucose? (Show your work)
   
   
   How would you make a dilution from the initial stock glucose solution that has a 2.5mM?  Describe the process and show all work.  This is your new stock solution.
   
   
   
2. Fill in the following table:
   When calibrating a pipet, count the number of drops required to fill a well.  Remember that if you change pipets that you MUST calibrate the new pipet.  In order to be accurate, you should obtain the same number of drops at least three times.

   Trial	drops of H2O	drops of glucose	Drops of reagent
   1 2 3 4 5 6
   Averages

   
   
3. Fill in the table below (see the key to the table below):

   Dc	Dw	Mc	Cw	Cc	Md
   0	5
   1	4
   2	3
   3	2
   4	1
   5	0

   Key:
   M_c = Molarity of the stock glucose
   M_d = Molarity of the diluted glucose
   D_c = Drops of the stock glucose solution
   D_w = Drops of water
   D_t = Drops of glucose + water (in this lab it should be 5)
   C_c = Drops of stock glucose to fill a well
   C_w = Drops of water to fill a well

   Formula:

4. Use the reaction sheet on the next page to perform the dilutions. 
   
   
   
5. Collect a sample of unknown from the teacher.  Add 20 drops of reagent to 5 drops of sample and assign a region into which each sample falls.

   Sample Number	Region

   Reaction Sheet:  After adding the respective amounts of glucose and water add 20 drops of reagent to each of the reactions. Use an empty pipet to gently mix the solutions. Wait 5 minutes for the color to develop fully.  Describe what you observed.

   Drops of water	Drops of glucose	Reaction
   5	0
   4	1
   3	2
   2	3
   1	4
   0	5

6. State the difference between a qualitative and a quantitative test as it has related to what you have done so far in lab.  What would be the advantage to using a qualitative test over a quantitative?  What would be the disadvantages?
7. 1. What is Beer’s law?
   2. When and why would you use it?
   3. The following are actual data obtained from Ms. Kucklick using a spectrophotometer to determine the absorbances of samples.

      mg/dL glucose	Absorbance
      0	0.0000
      50	0.0779
      100	0.1622
      200	0.3358
      300	0.5077
      400	0.6688

   4. Using the data from the previous table.  Interpret the plot using Beer’s law in the space provided below.

      A b s o r b a n c e	0.6
      	0.5
      	0.4
      	0.3
      	0.2
      	0.1
      		100	200	300	400
      		Concentration Glucose mg/dL

   5. What do the data show you?  Is it a straight line?  Determine the equation of the line.
   6. Given that the absorbance of a sample was _____, what would you conclude the concentration to be?  How did you determine this?
   7. Knowing what you do now, what would be the advantages to using a quantitative test over a qualitative?  What would be the downfalls?

Laminar and Turbulent Flow Laboratory

Objectives:

• The student should be able to use algebra to manipulate algebraic expressions.
• The student should be able to determine the effects of changing variables on algebraic equations.
• The student should be able to determine the theoretical maximum height that would give them laminar flow.
• The student should be able to go in the laboratory and construct a system that would give them laminar flow based on their calculations.

Equations needed:

Variables:

Materials supplied:

1 - Y - connector

2 - Bottles with 0.5 cm hose attached at the bottom

3 - 1 meter lengths of 0.5 cm hose

5 - connectors

2 - flow regulators

2 - 1 liter colored water (yellow and blue)

1. Looking at the above equations, you do not have all the necessary information to solve the Reynold’s flow equation.
   1.                   You are missing the average velocity.  Find and solve an equation for the average velocity.
   2.                   Plug the average velocity into the Reynold’s equation.
   3.                   Reduce the above equation and rewrite.
   4. What variable are you now lacking information for?  ______  Find and solve an equation for that variable.
   5. Plug the pressure variable into the Reynold’s equation.
   6. Reduce the above equation and rewrite.  This is your final equation.
2. Use the equation that you derived to answer the following questions.
   1.            What happens to the magnitude to the Reynold’s number upon doubling the following variables?

      r
      z
      D
      DL
      m
      g

   2. Changing which variables had the greatest affect?
   3. Which variables are the easiest to change?
   4. Given the fact that you are given a specific diameter and length of hose, what’s the only variable that you have control?
3.          Determine the maximum theoretical height needed to guarantee laminar flow.
   1. Plug all the known values in the equation from 1.f) and calculate N_Re.  (Don’t forget that you are also looking for a height.)
   2. Given that a Reynold’s number less than 2100 is consistent with Laminar flow, what is the maximum change in height that will guarantee you Laminar flow?  _______
4. Draw an ideal set up of the system including all details. 
5. Below are questions to guide your development of the ideal set up.
   1.             _____  Does the diagram include all lengths?
   2.             _____ When calculating the maximum height, did you subtract the height of the end of the hose from the height of the fluid in the bottle?
   3.             _____  What will happen if the end of the hose is higher than the upper level of the water?
   4.             _____  What do you think will happen if the hoses aren’t straight?
   5.             _____  If there are air bubbles in the hose, what do you think will happen?

Real Life Applications

Objective:

• The student should be able to integrate the information from the two previous laboratories and come up with a plausible system for measuring glucose in blood serum with a fluid flow system.

1. In order to modify the fluid flow system to handle small blood serum samples, which of the following would you modify?  How?  What affect would that change have?
   1. The diameter of the tube
   2. Length of the system
   3. Change in height
2. Would you want laminar or turbulent flow in the system?  Why?
3. What would be the advantage to designing a system that ran multiple blood chemistries in a matter of minutes with little waste?
4. Based on the answers to the previous questions, draw and label a fluid flow system design, which will determine the blood serum glucose levels for a critical patient in the emergency room.

APPENDIX A

SYMBOLS USED IN THE DERIVATIONS OF FLUID FLOW EQUATIONS

APPENDIX B

DERIVATION OF PRESSURE EQUATION

If all the vertical forces on a given volume of static liquid (the shaded area) are added together they must equal zero yielding the expression: Simplify the equation by removing S: Upon integration, assuming r to be constant throughout the column, or between two definite heights: If using SI units, gc = 1. If using English units,

APPENDIX C

DERIVATION OF PRESSURE DUE TO SKIN FRICTION

Given the following formulas:

• Relationship between skin friction parameters:
  
  
  
• Laminar flow of Newtonian fluids (a Newtonian fluid is an ideal fluid):
  
  
  
• Average velocity for newtonian fluid:
  
  

Derivation for the Hagen-Poiseuille Equation:

Solve the following equation for t_w

 à 

Substitute t_w in the average velocity equation:

Solve for Dp_s:

Converting radius to diameter:

Therefore:

APPENDIX D

DERIVATION OF REYNOLD’S EQUATION

Reynold’s Number Derivation:

Since:

Solve for t_w:

By definition:

After substituting t_w into the above equation:

By definition:

Then rearrange the Dp_s equation solving for the average velocity:

Plug the average velocity equation into the Reynold’s equation:

Plug in the equation for Dp of Appendix B for Dp_s:

The final equation shows which variable makes the greatest difference when designing a fluid flow system.

APPENDIX E

MULTISTAT III+ EXPERIMENT

This experiment was run at 500 nm at 30°C. A ratio of 3 mL of glucose to 216 mL of reagent was added to a final volume of 240 mL. The absorbances are end point values.