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									                                          Engineering Exercise
                             By Drs. Stephanie Farrell and Robert P. Hesketh
                                         Chemical Engineering
                                               Fall, 2003
Introduction

The human body is an exquisite combination of interacting systems that can be analyzed using
engineering principles. For instance, the heart is a pump that pumps blood throughout the circulatory
system, which is analogous to a network of pipes. Pumps and piping systems are studied by many
types of engineers.

In this experiment, you will investigate the function of the lungs, the heart, and the cells using basic
engineering principles that are related to fluid flow, pumps and piping systems, and chemical reactions.
You will take measurements, use estimates, and apply correlations to calculate important physiologic
quantities such as blood pressure, the rate of oxygen consumption, rate of blood flow, and the rate of
energy used. You will compare your results for resting and exercise conditions.

Terminology and Concepts

Heart Rate is the number of heart beats per minute.

      Resting heart rate should be measured by listening to the heart using a stethoscope placed at
       the crease of the elbow. To obtain an accurate measurement, count the number of beats in 30
       seconds and multiply by two to convert to beats per minute.

      Heart rate during exercise can be measured using the automatic heart rate monitor on the
       exercise equipment. These monitors tend to be more accurate for the elevated heart rates that
       are observed during exercise, and they are less accurate for resting heart rates.

Blood Pressure is the force exerted by the blood on the walls of an artery. Blood pressure is
measured by a device called a sphygmomanometer (see attached instructions). Blood pressure
measurements involve two readings: systolic and diastolic. The systolic blood pressure is the higher
reading that occurs when the heart is pumping. Diastolic blood pressure is the lower value that occurs
when the heart is filling. Blood pressure is conventionally expressed in units of mm Hg.

Breathing rate is the number of breaths taken in one minute. The most difficult thing about measuring
the breathing rate is for the subject to breathe naturally. There is a tendency to breathe slower and
deeper than normal. Try to breathe as normally as possible, and count the breaths taken over a period
of at least one minute.

Fluid Pressure: Fluids exert pressure downward – consider the pressure felt by a diver as he or she
goes deeper into the water. The water pressure at the bottom of the sea is much higher than the
pressure at the surface. The air pressure at the top of a mountain in Boulder, CO is much less than the
air pressure in Glassboro, NJ. This is due to the weight of the fluid.

For this reason, sometimes pressure is expressed in units as simple as mm Hg – equivalent to the
downward pressure exerted by one mm of mercury, or cm H2O – equivalent to the downward pressure
exerted by one cm of water.

EQUATIONS AND EXAMPLE CALCULATIONS – Please note that measured values are in bold.
These numbers will be replaced by your data (or your own calculated values) for these
quantities.

1. Average Blood Pressure. Since the heart spends twice as long filling as it does pumping, the
   average blood pressure for the pumping-filling cycle can be calculated by:

                                           systolic  2 * diastolic
                                 BPavg                                                       (1)
                                                      3
                                          Engineering Exercise
                             By Drs. Stephanie Farrell and Robert P. Hesketh
                                         Chemical Engineering
                                               Fall, 2003
   For example, a typical blood pressure measurement is 120/65, corresponding to a systolic pressure
   of 120 mmHg and a diastolic pressure of 65 mm Hg. The average blood pressure would be:

                                  120 mm Hg  2 * 65 mm Hg
                        BPavg                              83 mm Hg
                                             3
                              
2. Oxygen consumption rate ( VO2 ) the rate at which the body uses oxygen, often expressed in units
   of mL O2/min or L O2/min. To perform this calculation, we need to know the volume of oxygen
   consumed in one breath. For this experiment, we will use a typical value of 20.8 ml oxygen per
   breath at rest and 60 ml oxygen per breath during moderate exercise such you would perform on
   the bicycle. Exercise on the treadmill tends to be more strenuous, causing the volume of oxygen
   used per breath to be about 100 ml.

                                         breaths   volume O 2 
                                   VO2                                                       (2)
                                          min   breath 
                                                                
For instance, if the breathing rate is 12 breaths per minute, the oxygen consumption rate at rest would
be:

                              breaths        ml O 2          ml O 2
                        VO2  12           20.8           249.6
                                 min  
                                               breath 
                                                                  min

                       
3. Blood flow rate ( V B ) is the volume of blood pumped through the body in one minute. Since the
oxygen consumed is carried to the body by the blood, the blood flow rate is related to the oxygen
consumption rate. By studying many people, scientists have determined that the blood flow rate is
related to the oxygen consumption rate by the following equation:

                                                L     
                                         VB  3      8VO2                                     (3)
                                                min
For example, if the oxygen consumption rate is 249.8 ml O2/min as calculated in the above example,

                              L              mL O 2  L          L
                       VB  3      8 * 249.8                5 min
                              min              min 1000 mL 

4. Energy Expenditure is the rate of energy consumption by the body. Energy expenditure is
typically expressed in units of kcal/min. Since oxygen is burned with food to create energy, the rate of
energy expenditure is related to the rate of oxygen consumption. The energy created by burning one
liter of oxygen is approximately 5 kcal.

                                              kcal  
                                        EE  5      VO2                                    (4)
                                              L O2 
For example, if the oxygen consumption rate is 249.8 ml/min as calculated in the example above,

                           kcal        mL O 2     L            kcal
                     EE  5      249.8         1000 mL   1.25 min
                           L O2         min            
                                          Engineering Exercise
                             By Drs. Stephanie Farrell and Robert P. Hesketh
                                          Chemical Engineering
                                               Fall, 2003
Energy expenditure is related to body weight. You can also estimate your energy expenditure at rest
(without measuring your rate of oxygen consumption) using the equation:

                                                   kcal             kcal
                             EErest  0.00483            * W  .467                              (5)
                                                  min lb            min
where W is your weight in pounds.

You can estimate your energy expenditure during exercise using the following general information.
Approximately 0.726 kcal per pound of body mass are expended for each mile of running. Therefore,
the rate of energy expenditure would be

                                                     kcal 
                                               0.726 mi lb W n 
                                 EE running                                                   (6)
                                                        t
where n is the distance run (in miles) and t is the time in minutes (the duration of the run)

5. Blood pressure at different elevations . To calculate the blood pressure at an elevation lower
than the heart, use the equation:

                                              P2  P1  gh                                      (7)
P1 = Pressure at lower level (bending over, with cuff below heart level)
P2 = Pressure at normal level (arm in relaxed position so the cuff is at the same level as the heart)
h =height difference between the two positions (measured at the end of the cuff, near the crook of the
elbow)
g = acceleration of gravity, 980 cm/s
 = blood density, 1.056 g/cm3
For example, if the average blood pressure at heart-elevation (measured in the arm, with the arm held
naturally) is 83 mm Hg, and the difference in elevation is 30 cm, the blood pressure at the lower
elevation (measured in the arm, with the arm extended downward) can be calculated by:

                                      g     cm                          mm Hg 
                83 mm Hg  P1  1.056 3  980 2 - 30 cm  7.524  10 4
                                                                                     
                                     cm     s                           g/cm s 2 
                                                                                      
                P  106.4 mm Hg
                 1


The last term on in parenthesis on the left side is just a conversion factor used to get pressure units of
mm Hg.
                                           Engineering Exercise
                              By Drs. Stephanie Farrell and Robert P. Hesketh
                                          Chemical Engineering
                                                Fall, 2003
Procedure: Perform and record the following measurements. All data must be neatly recorded
in a laboratory notebook.

At rest
   1. Breathing rate (count the number of breaths in one minute)
   2. Heart Rate (Use stethoscope to listen for pulse. Count beats per minute.)
   3. Blood Pressure
           a. With arm relaxed at normal elevation.
           b. Bending over at the waist with arm hanging vertically (“touch your toes” position).
              Record the difference in arm elevation in parts a and b. The difference should be
              approximately -30 cm.
During Exercise
This is a very mild exercise in which you will jog a couple of laps around the engineering “track”, until
you feel that your breathing rate has increased a little. Don’t sprint – results will not be accurate. FYI, a
lap around the “track” is 820 feet or 0.1553 miles.
Put on the TIMEX heart rate monitor and speed/distance systems as shown by your instructor.
   4. Distance and time using as measured by the Timex system (use Chrono Mode).
   5. Breathing rate (immediately after exercise)
   6. Heart Rate using the Timex system (use summary mode to display average HR for duration of
      exercise).
Calculations: Perform the following calculations and show your units on all calculations!
At rest
   1. Average Blood Pressure (Equation (1))
           a. Normal elevation
           b. Arm lowered
   2. Expected blood pressure in lowered arm (P1) using Equation (7). Compare with the average
      blood pressure that was calculated in the previous question.
   3. Rate of oxygen consumption using Equation (2). For your calculation, use a value of 20.8 ml
      oxygen per breath at rest.
   4. Blood flow rate using Equation (3)
   5. Energy Expenditure – calculate two ways and compare the results.
           a. calculate resting energy expenditure rate from the measured oxygen consumption rate
              (Equation (4))
           b. estimate your resting energy expenditure from your body weight (Equation (5)).
           c. compare these two values of energy expenditure.
                     1. What is the % difference between the two values?
                     2. Discuss why might the values be different. (On what measurements are the
                        values based? For each equation used, what physiologic variables were
                        estimated using “typical” values?
                                         Engineering Exercise
                            By Drs. Stephanie Farrell and Robert P. Hesketh
                                        Chemical Engineering
                                              Fall, 2003
During Exercise
   6. Rate of oxygen consumption Equation (2). For your calculation, use a value of 60 ml oxygen
      per breath during moderate exercise.
   7. Blood flow rate (Equation (3))
   8. Energy Expenditure – calculate two ways and compare the results.
          a. calculate energy expenditure from the estimated oxygen consumption rate after exercise
             (Equation (4))
          b. estimate your energy expenditure during running by the equation for EErunning given
             above (Equation (6))
          c. compare these two values of energy expenditure.
                   1. What is the % difference between the two values?
                   2. Discuss why might the values be different. (On what measurements are the
                      values based? For each equation used, what physiologic variables were
                      estimated using “typical” values?
Assignment: Due next week at the beginning of class. One assignment per team.
   1. Submit the yellow laboratory data sheet from your notebook
   2. Submit your calculations and answers to the above questions, written neatly and showing units
      throughout your calculations.
                                           Engineering Exercise
                              By Drs. Stephanie Farrell and Robert P. Hesketh
                                          Chemical Engineering
                                                Fall, 2003
                                        Measuring Blood Pressure

Blood pressure is the force of blood against the walls of the artery. You may be asked to monitor your
blood pressure at home because your office readings show that you have hypertension, or high blood
pressure. Remember, your blood pressure changes during the day, according to the needs of your
body. For example, blood pressure goes up when you exercise and goes down when you are resting or
sleeping.

You will be measuring the blood pressure in your brachial artery, a blood vessel that goes from your
shoulder to just below your elbow. The blood pressure monitor will show two different pressure
readings. The systolic pressure is the highest pressure in an artery when your heart is pumping blood
to your body. The diastolic pressure is the lowest pressure in an artery when your heart is at rest.

What do I need to do before I measure my blood pressure?

   1. Place your arm, raised to the level of your heart, on a table or a desk, and sit still.

   2. Wrap the correctly sized cuff smoothly and snugly around the upper part of your bare arm. The
                      cuff should fit snugly, but there should be enough room for you to slip one
                      fingertip under the cuff.

   3. Be certain that the bottom edge of the cuff is 1 inch above the crease of your elbow.

   4. Rapidly inflate the cuff by squeezing the rubber bulb to 30 to 40 points higher than your last
      systolic reading (about 150 mm Hg should be enough). Inflate the cuff rapidly, not just a little at
      a time. Inflating the cuff too slowly will cause a false reading.

   5. After the cuff is inflated, the automatic mechanism will slowly reduce the cuff pressure.

   6. Write down your blood pressure, putting the systolic pressure before the diastolic pressure. You
      would write down a number such as 120/80. Also record your pulse rate (heart beats per
      minute)

   7. Press the exhaust button to release all of the air from the cuff.

   8. Turn off the machine.

   9. If you want to repeat the measurement, wait two or three minutes before reinflating the cuff.

This handout is provided to you by your family physician and the American Academy of Family
Physicians. [8/96]

								
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