Laboratory Unit

Course: KINE xxxx  Exercise Physiology KINE xxxx Exercise Physiology Edit attributes for this course (KINE xxxx  Exercise Physiology)
Module: Laboratory Unit 6 Laboratory Unit Edit this module (Laboratory Unit)
Lesson: Lab 1 - Work, Power, Efficiency and Economy 1 Lab 1 - Work, Power, Efficiency and Economy Edit this lesson (Lab 1 - Work, Power, Efficiency and Economy)
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I. Introduction

Welcome to the first laboratory assignment of the course. This lab will help you understand the basic tests used to determine work, power, mechanical efficiency, running economy, and the calculations involved in obtaining the results for each. Some of these tests require specialized equipment found only in the laboratory setting, but some can be completed in field settings with relatively inexpensive equipment.

The primary goals of this lab are to help you understand the concepts involved with work and power, and give you some suggestions on tests that can be used by the teacher or coach.

 

Learning Objectives

After completion of this lab, you should be able to:

1. Calculate work and power during a step test.

2. Calculate work and power during a test on a cycle ergometer.

3. Calculate mechanical efficiency.

4. Describe the standard Wingate Anaerobic Power Test.

5. Calculate peak power, mean power, and fatigue index during a standard Wingate Anaerobic Power Test and compare the results to appropriate norms.

6. Calculate and express running economy in ml/kg/m and in m/ml/kg and compare results to appropriate norms.

 

Outline of Lab I Content

I.   Measurement of External Work and
     Power Output (P. 2-5)

      A.   Step Test

      B.   Cycle Ergometer

II.  Measurement of Mechanical Efficiency (P. 6-7)

III. Measurement of Short-term Power - The Wingate
     Anaerobic Power Test (P. 8-14)

IV. Measurement of Running Economy (P. 15)

V.  Links to Equipment Vendors (P. 16)

VI. Assignment (P. 17)

 

 

 
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I. Measurement of External Work and Power Output

A. The Step Test  

One of the simplest tests for measuring work and power is a step test.  Before you begin reading, you should review the formulas for determining work and power.

Work = force X distance

Power = work/time 

The picture depicts a person (Dr. Schwane) who weighs 77 kg stepping up onto and down off of a bench that is 45 cm (0.45 m) in height. Assuming that this person is standing perfectly upright both when on the floor and when on the step, he lifts his body weight of 77 kg vertically upward a distance of 0.45 m with each step. Counting only this external work in lifting the body upward, this person does 34.65 kgm of work with each step:

W = F x d = 77 kg x 0.45 m = 34.65 kgm

(NOTE: Technically, the kilogram is a unit of mass and not a unit of weight or force. For this reason you sometimes see reference to “kiloponds [kp]” to indicate units of force. Numerically the kilopond and the kilogram are equal. For simplicity, I will use kilogram as though it were a unit of force, since in practice we use kilograms as weight units, just as we do pounds, and weight is a force.)

I hope it is obvious that a lighter person would do less work stepping up on this same step, and a heavier person would do more work with each step. I hope it is also obvious that the amount of work can be changed by varying the height of the step.

 

 
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I. Measurement of External Work and Power Output (cont.)

Power output is also easily determined with a step test. We simply need to know the number of times an individual steps up onto the step in a given period of time. Let’s continue with the previous example and assume that Dr. Schwane steps at the rate of 15 steps/minute. In this scenario:

Power output = (34.6 kgm/step) x (15 steps/min) =  519 kgm/min

This power output is equivalent to 85 watts or 1.19 kcal/min. (Refer to convert in Glossary if necessary.)

Determination of power output with a step test as described here has important limitations: It ignores the negative work of lowering the body weight during the step down from the bench, as well as the slight forward and backward movement of the body with each step.

 

 
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I. Measurement of External Work and Power Output (cont.)

B. The Monark Bicycle Ergometer  

One of the most useful exercise devices for studying work and power is the mechanically braked bicycle ergometer.  The picture of the bicycle ergometer above is made by Monark, a Scandinavian company. Different models of this bike can be purchased from various vendors. Prices start at about $600 and go much higher, depending on quality, computerization, and the like. At the end of this lab is a list of vendors that sell ergometers and assorted other equipment related to physiological testing.

If used properly, the Monark bike accurately measures external work done, and it is simple to use. Work on the Monark bike is determined according to the basic work equation: 

Work = force x distance

The force is a friction resistance provided by a belt around a large flywheel. This belt can be tightened to varying degrees to apply different amounts of resistance. The person pedaling the bike must exert muscular force to overcome this resistance and thus do external work. The amount of friction resistance is indicated on a scale just below the flywheel. Resistance is measured in kilograms (or kiloponds; see earlier note).  

Distance in the work equation is the distance that a point on the flywheel moves against the friction resistance. One revolution of the flywheel is equal to a distance of 6.0 meters, therefore every time the pedals of the bike make one complete revolution, the flywheel moves 6.0 meters. If the friction resistance is set at  2 kg, then 12 kilogram-meters (kgm) of work is done with each pedal revolution:

Work = force x distance = 2 kg x 6 m/rev = 12 kgm/rev);

If the resistance is set at 5 kg, then:

Work = 5 kg x 6 m/rev = 30 kgm/pedal revolution; and so forth.

 

 
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I. Measurement of External Work and Power Output (cont.)

To determine power we simply need to know how many pedal revolutions are done in a given period of time. The Monark bike has a tachometer near the handle bars that tells the pedal revolutions per minute (rpm). Another common method for controlling pedaling rate is to set a metronome that the exerciser follows. If we want very precise measurements of work and power, we actually count pedal revolutions and time them with a stopwatch (or better yet, interface the bike with a computer that will count each pedal revolution).

EXAMPLE for determining power using a bicycle ergometer:

A person pedals a Monark bike at the rate of 50 rpm with a friction resistance of 3 kg on the flywheel. What is the power output?

Power = work ¸ time = (force x distance) ¸ time = 3 kg x (6 m/rev) x (50 rev/min) = 900 kgm/min

Bicycle ergometers other than the mechanically braked (frictional resistance) Monark are available from various vendors. There are several rather sophisticated electronic bicycle ergometers. These maintain a given power output regardless of the pedaling rate, which is an advantage in certain tests. These ergometers cost much more than the standard mechanically braked Monark ergometer. There are also many brands and models of electronic and mechanical bicycles that are intended for general fitness training. Most of these are not ergometers, because they do not provide accurate settings of work or power.

 

 
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II.  Measurement of Mechanical Efficiency

By measuring oxygen consumption (VO2) during exercise on a bicycle ergometer, mechanical efficiency can be determined. VO2 can be converted to energy units to give power input, so long as the exercise does not require oxygen at a rate greater than the highest rate at which a person can consume oxygen (i.e., VO2max).

As a rule of thumb, 1 liter of oxygen consumed is equivalent to 5 kcal of energy “turned over” in aerobic metabolism (i.e., transformed from one form to another or transferred from one chemical substance to another in aerobic metabolism). Therefore, for example, if we know that a person's VO2 is 2.5 L/min, we know that this person is turning over energy at the rate of 12.5 kcal/min (2.5 L of oxygen x 5 kcal/L of oxygen).

We will deal with some of the specifics related to measuring oxygen consumption in another lab.

 

 
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Mechanical Efficiency (cont.)

Let’s assume that we are measuring oxygen consumption during a test on a Monark ergometer, as shown in the picture. Assume that the following data were measured during the third minute of the test (i.e., after initial metabolic adjustments had occurred and the person was in a relatively steady state):

resistance on flywheel = 2.5 kg; pedaling rate = 60 rpm; VO2 = 1.91 L/min.

This person’s overall or gross mechanical efficiency during this exercise was 22%. You may want to do the calculations and see if you get this same result before going ahead to the explanation of the calculations.

Explanation of calculations:

Power output = (F x d) ¸ time = 2.5 kg x (6 m/rev) x (60 rev/min) = 900 kgm/min

This power output is equivalent to 2.1 kcal/min (900 kgm x 0.0023 kcal/kgm).

Power input = (1.91 L O2/min) x (5 kcal/L O2) = 9.6 kcal/min.

Efficiency = (Pout / Pin) x 100 = (2.1/9.6) x 100 = 22%.

Note what this efficiency value of 22% means: Of the total energy turned over in metabolism (i.e., 9.6 kcal/min), only 22% (i.e., 2.1 kcal/min) was transformed to useful external work, in this case turning the flywheel of the bike. The rest of the energy, 78% (7.5 kcal/min), was wasted in terms of doing work on the bike. Another way of looking at this is: To do the equivalent of 2.1 kcal/min of external work on the bike, the exerciser had to turn over a total of 9.6 kcal/min in metabolism, more than four times as much energy. 

 
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III. Measurement of Maximal Short-term Power—The Wingate Anaerobic Power Test

In theory, the Monark bike can be used to measure maximal short-term power in athletes, to compare different athletes and to compare changes over time (e.g., changes with training or recovery from injury). For example, a given resistance could be set and the athlete would pedal as many times as possible in a given time period; “maximal power” could then be calculated. Unfortunately, this cannot be done with the standard Monark bike because resistance would not stay constant during such a test. There is a simple modification that can be made, however, to keep resistance constant. That is to connect the friction belt to a pulley system to which weights can be added.

For example, instead of tightening the belt to give 2 kg of resistance by means of the regular mechanism, a 2-kg weight is hung on the pulley system to give the same resistance on the flywheel. With this system the resistance stays constant no matter what the rate of pedaling is.

 

 
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III. The Wingate Anaerobic Power Test (cont.)

This system is used in a very useful test known as the Wingate Anaerobic Power Test. The test is called a test of anaerobic power because most of the energy (about 75-85% of the total energy input) for exercise such as is done in this test comes from anaerobic metabolism.

In brief, the standard Wingate Test is a maximal 30-second cycling test. Three variables are commonly measured:

(a) peak power, the highest power at any time during the test;

(b) mean power, the average over the entire 30 seconds (mean power indicates the ability to maintain high power over 30 seconds); and

(c) fatigue index (also referred to as % power decline). Fatigue index is calculated as follows: ([peak power - lowest power] / peak power) x 100.

In the Wingate Test, peak power comes within the first 5-10 seconds and then power gradually decreases over the rest of the test as the subject fatigues. Peak power and mean power may be expressed in absolute terms (usually in watts) or relative to body weight (watts/kilogram of body weight).

 

 
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III. The Wingate Anaerobic Power Test (cont.)

Important aspects of Wingate Test administration include:

(a) Assuring plenty of warm-up prior to the test;

(b) instructing and motivating the athlete to give maximal effort throughout the test;

(c) selecting the proper resistance to elicit maximal power (the resistance can be too little or too much); a general guideline is to use 0.075-0.105 kg per kilogram of body weight;

(d) accurately counting pedal revolutions over 5-second or shorter segments of the test; this can be done reasonably well by manual counting, but a computer-based system is obviously much better; and

(e) having the athlete accelerate to maximal pedaling rate with a lighter resistance before applying the final resistance just prior to the measurement period.

 

 
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The Wingate Anaerobic Power Test (cont.)

Norms (average values) are available for various groups of athletes for peak power and mean power. Many of these norms were generated on athletes and nonathletes in Israel, where this test originated. Following are some of these norms.

Peak Anaerobic Power and Mean Anaerobic Power for Athletes and Healthy non-Athletes (watts/kg)
  Peak Power Mean Power

Male Athletes

   
Rowers 11.7 10.5
Sprinters and Jumpers 11.6 9.2
Weight-lifters and Wrestlers 10.2 8.7

Female Athletes

Sprinters and Jumpers 9.5 8.1
Gymnasts 9.0 7.5
Swimmers 8.8 7.2

Healthy Untrained 18-25 year-old Males

  8.2-8.8 6.9-7.3

Healthy Untrained 18-25 year-old Females

  8.3-8.8 5.5-5.8

The coach or teacher who uses this test would want to develop his/her own norms on the athletes and students in his/her program.

 

 
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The Wingate Anaerobic Power Test (cont.)

A thorough description of the Wingate Test, including norms for various groups, is given in the book: Inbar, Bar-Or and Skinner, The Wingate Anaerobic Test (Human Kinetics, 1996), ISBN 0-87322-946-0 (price = ca. $20.00).

The test can be done fairly easily and accurately by adapting a standard Monark bicycle ergometer. For greater accuracy and automation, however, hardware and software are available for interfacing a Monark bike to a personal computer. One company that sells this instrumentation is Vacumed (http://www.vacumed.com/).

 
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The Wingate Anaerobic Power Test (cont.)

Following are summary results of a standard 30-second Wingate Test of anaerobic power of the legs. This test was done on a 16-year-old female gymnast who weighed 110 pounds (50 kg). The resistive load was 4.25 kg.

Summary of Results for 30-second Wingate Test

Time Interval (sec) Pedaling Speed (rpm) External Power Output
0:00-0:05 108 2754 kgm/min 
(450 watts)
0:05-0:10 102 2601 kgm/min 
(425 watts)
0:10-0:15 94 2397 kgm/min 
(392 watts)
0:15-0:20 86 2193 kgm/min 
(358 watts)
0:20-0:25 79 2014 kgm/min 
(329 watts)
0:25-0:30 72 1836 kgm/min 
(300 watts)

Peak Power = 450 watts (9.0 watts/kilogram of body weight)

Mean Power = 376 watts (7.5 watts/kg)

Fatigue Index (% Decrease) = ([2,754 - 1,836] ¸ 2,754) x 100 = 33.3%

The values obtained for peak power and mean power match the norms given above for Israeli female gymnasts. The fatigue index indicates that peak power declined by 33.3% during the test. Or, in other words, the lowest power, during the last 5 seconds of the test, was 66.7% of the peak power. (Actually, a drop-off of power of only 33% is quite good.)

 

 
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The Wingate Anaerobic Power Test (cont.)

A couple of final points:

Note that power measured during the Wingate Test is power output. If, for example, efficiency = 20% during the test, power input is five times the power output. Obviously, there has to be a very high rate of energy turnover by the body to produce high power output during this test or any similar activity.

By adjusting the position of the bike, the Wingate Test can also be used to test power of the arms. The test can also be modified to test power over varying periods of time (e.g., 20 sec, 60 sec). Norms may not be available for such tests, however.

 

 
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IV. Measurement of Running Economy

Economy of running is an important determinant of success in distance running. Running economy is easy to measure in a laboratory. It simply involves measuring VO2 during running. Unfortunately, there is no accurate way to estimate economy without actual measurement of VO2.  The picture illustrates a person running on a treadmill with VO2 being measured by so-called pulmonary gas exchange. (We are not concerned about the details of measuring VO2 in this lab; these will be addressed in another lab.)

Let’s assume that this person is running at 8.0 mph (214 m/min). Also, her steady-state VO2 = 46.0 milliliters of oxygen per kilogram of body weight per minute (ml/kg/min). Her economy of running at 8.0 mph can be described in three ways:

(a) Simply with the VO2 value of 46.0 ml/kg/min.

(b) As milliliters of oxygen consumed per kilogram of body weight per meter run. This is determined by dividing VO2 (ml/kg/min) by running speed (m/min): 46.0 ml/kg/min / 214 m/min = 0.21 ml/kg/m. In other words, on average, every kilogram of this person’s body consumes 0.21 ml of oxygen for each meter run.

(c) As meters run per milliliter of oxygen consumed per kilogram of body weight. This is determined by dividing running speed (m/min) by VO2 (ml/kg/min): 214 m/min / 46.0 ml/kg/min = 4.7 m/ml/kg. In other words, this person covers 4.7 m for each milliliter of oxygen consumed by each kilogram of her body.

Referring to these ways of expressing economy, the runner would be more economical if she (a) had a lower VO2,  (b) had a lower VO2 relative to body weight for a given distance run, and (c) could run a greater distance for a given VO2 relative to body weight. Highly trained endurance runners are more economical than others. They will typically have economy values ranging from 5.0 m/ml/kg (0.20 ml/kg/m) to 6.0 m/ml/kg (0.16 ml/kg/m) when running at speeds of 9.0 – 11.0 mph.

 

 
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Vendors that sell assorted instruments related to exercise physiology in general and ergometry in particular:

Creative Health Products (http://www.chponline.com/)
Lafayette Instruments (http://www.licmef.com/)
Quinton (http://www.quinton.com/)
Vacumed (http://www.vacumed.com/)

This list is certainly not exhaustive. I suggest you go to the site of Vacumed or Creative Health Products to get a feel for the types of equipment that can be purchased from these companies. Also, check the prices of different models of Monark bicycle ergometers. You may want to conduct an Internet search for "Monark," to make price comparisons.

 
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VI. Laboratory Assignment

Complete the following. Submit written responses, as required, to the Instructor as an attachment to an e-mail. Show enough details of mathematical calculations to indicate how answers were derived.

1. Conduct a 2-minute step test. Make appropriate measurements to calculate work and power. Describe pertinent details of your test, and submit both raw data and calculated values for work and power.

2. Discuss: Could you use a short step test (e.g., 10-30 sec) as a test of power to compare athletes? If “No,” why not? If “Yes,” briefly describe the test and the calculation of test results you would use for comparing athletes.

3. A person pedals a standard Monark bike at the rate of 75 rpm with a friction resistance of 2.5 kg on the flywheel. What is the power output in kgm/min and in watts?

4. If the person in Item 3 had a VO2 = 2.25 L/min while exercising on the bike, what was his mechanical efficiency?

5. A Wingate Test of anaerobic power of the legs was done on a 23-year-old male weight-lifter who weighed 93 kg. A resistive load of 7.0 kg was used. Following are the pedaling rates by 5-second intervals. Calculate peak power, mean power, and fatigue index, and compare this person's results with norms given above.

0:00-0:05 - 150 rpm

0:05-0:10 - 141 rpm

0:10-0:15 - 134 rpm

0:15-0:20 - 116 rpm

0:20-0:25 - 107 rpm

0:25-0:30 - 97 rpm

6. Assume that the person in Item 5 had a mechanical efficiency = 21% during the Wingate Test and calculate the total amount of energy (in kcal) this person turned over in metabolism during the test.

7. A high school cross-country runner was tested in a lab during running on a treadmill. When running at a pace of 6:30 per mile, his VO2 was 55.2 ml/kg/min. What was his economy in ml/kg/m? In m/ml/kg? How would you describe this runner’s economy compared with economy of elite runners?

8. Give an example of the weight a person you know can lift in a maximal bench press. Estimate the distance the barbell is lifted during this bench press. Using these data, calculate the external work done during this single lift. Then, assume that this person’s mechanical efficiency = 25% during the lift, and calculate the amount of energy (in kcal) this person must turn over in metabolism to do the single lift.

9. Calculate the external work that must be done for you to climb a flight of stairs from the first floor to the second floor of a building (give the raw data that you use in your calculation). Then, assume that your mechanical efficiency when stair-climbing = 23%, and calculate the amount of energy (in kcal) you must turn over in metabolism to climb the flight of stairs.

 

 
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You have reached the end of Lab 1.

 
 
Lesson: Lab 2 - Measurement of Oxygen Consumption 2 Lab 2 - Measurement of Oxygen Consumption Edit this lesson (Lab 2 - Measurement of Oxygen Consumption)
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Introduction

The goal of lab 2 is to facilitate understanding of how whole-body oxygen consumption (VO2) is measured. Measuring the rate at which oxygen is consumed is a powerful tool in understanding a person’s metabolism at rest and especially during exercise. VO2 reflects the contribution of aerobic metabolism to the total energy input. There is no similar variable that can be measured to indicate the contribution of anaerobic metabolism. This lab will focus on aspects of measuring VO2. In another lab we will work with specific responses of VO2 in different situations.

 
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Learning Objectives

After completion of this lab the student should be able to:

1.    List basic equipment that is needed to measure oxygen consumption.

2.    Define abbreviations commonly used in pulmonary gas exchange measurements.

3.    List variables that must be measured in order to determine oxygen consumption.

4.    Discuss the basic concept of VO2 as the difference between volume of oxygen breathed in and volume of oxygen breathed out.

5.    Discuss the basic concept of VCO2 as the difference between the volume of carbon dioxide breathed in and the volume of carbon dioxide breathed out.

6.    Discuss the concept of expressing gas volumes such as VO2 related to a standard set of conditions, including why this is necessary.

7.    Given pertinent data, calculate VO2 and VCO2.

NOTE:  You are not expected to memorize specific equations presented in this lab.  You are expected to be able to use equations in calculations and to understand the concepts that  related to the equations.

 

 
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List of Abbreviations

Below is a list of common abbreviations used in discussing measurement of oxygen consumption.  These abbreviations are used in this lab and throughout the course. Abbreviations are part of the vocabulary of a discipline. Just like learning vocabulary in the study of a foreign language, it is essential that you become familiar with these common definitions (and others that will come up in the course). This will greatly facilitate your studying and learning of the concepts.

An important note: As stated below, the letter "V" is the abbreviation for "volume." Sometimes we will be interested in the total volume of a gas, such as the total volume of oxygen consumed by a person (e.g., in liters). More often, we want to know the rate at which some gas is flowing or being used, such as the rate at which oxygen is being consumed by a person (e.g., in liters per minute). According to standard use, a dot is placed over the V to indicate a rate of flow, distinguishing it from volume (a V with no dot). For example, to indicate a rate of flow or use of oxygen, the following symbol is used:

For technical simplicity in this course, I will not put dots over Vs (or other letters) to indicate rates. Rather, I will use V for both volume and flow rate, and I will indicate which variable is intended by the unit (e.g., V = 75 liters, a volume, and V = 75 liters per minute, a rate of flow.

V - volume or rate of flow of a gas. 

VO2 - volume of oxygen consumed or volume of oxygen
           consumed per minute.

VCO2 - volume of carbon dioxide produced or volume of
              carbon dioxide produced per minute.

VI - volume of air inspired or volume of air inspired
       per minute.

VE - volume of air expired or volume of air expired
        per minute.

FIO2 - fraction of oxygen in inspired air.

FEO2 - fraction of oxygen in expired air.

FICO2 - fraction of carbon dioxide in inspired air.

FECO2 - fraction of carbon dioxide in expired air.

FIN2 - fraction of nitrogen in inspired air.

FEN2 - fraction of nitrogen in expired air.

 
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Overview of Equipment

In this section you will be introduced to the basic pieces of equipment that are used in many systems for measuring whole-body oxygen consumption.  There are many possible systems using combinations of different individual pieces of equipment.  The pieces of equipment presented here are basic items that are typical of traditional systems that can be used in a simple, manual mode.  These can also be interfaced with a computer to have more automated systems.  In addition, there are a number of highly automated all-in-one systems that range in cost from about $10,000 to about $100,000.

 

 
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Overview of Equipment (cont)

Gasometer:  Shown in the above picture is a Collins 120-liter gasometer.  Literally a "gas measurer," the gasometer measures gas volumes very accurately.  Gas is stored inside the cylinder that raises and lowers.  In the left hand view, the cylinder is empty. In the right hand view there is gas being stored inside the elevated inner cylinder. Gas in this cylinder is sealed from the environment by water in the outer cylinder.  Gas volume is determined by the difference in heights of the cylinder at the beginning and end of measurement.  The Collins gasometer can be used for directly collecting a sample of expired air from a subject over a timed period.  Volume of the sample can be determined, and then a portion of the sample can be run through gas analyzers to determine percentages of oxygen and carbon dioxide.

 

 
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Overview of Equipment (cont)

Dry gas meter.  A dry gas meter, just like those used to measure the use of natural gas in homes and buildings, can be used to measure volumes of gases breathed by a subject.  These are usually used only on the inspired side of the subject; that is, the subject breathes in room air through the meter.  Breathing out through the meter results in collection of moisture in the meter, which may interfere with its functioning and will shorten its useful life.  Also, it is difficult to disinfect the meter, so it would not be good to use the meter on the inspired side after it has been used on the expired side.  Volumes are determined by the difference between starting and ending readings on the meter dial.

 

 
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Overview of Equipment (cont)

Douglas-type gas collection bags.  Shown is a 120-liter plastic bag with a valve that controls access of gas into and out of the bag.  These bags allow simple collection of expired air in many settings, and then gas can be stored in the bags for hours before analysis, if necessary.  These bags are only useful for collecting and storing gas samples.  Volume of gas in the bag must be measured by another instrument, such as the Collins gasometer.

 

 
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Overview of Equipment (cont)

Two-way nonrebreathing valve assembly.  The valve assembly shown allows very high flow rates, such as occur during intense exercise, with little resistance. This valve assembly controls the direction of air flow so all inspired air comes from one side (the left side in this picture), with no expired air going back in that direction. All expired air goes out the other direction (to the right in this picture) without mixing with inspired air (i.e., no expired air is "rebreathed"). 

IN >>> >>> OUT

An exploded view of the nonrebreathing valve assembly is shown below.

Direction of gas flow is controlled by the two one-way check valves that the technician is holding in the picture. The pictures below are close-ups of these one-way check valves. In the left hand picture, she is able to open the check valve by applying gentle finger pressure in the direction shown, but in the right hand picture the valve does not open in the opposite direction. These two check valves working in tandem enable the nonrebreathing valve assembly to allow air to be inspired from only one side and air to be expired to only the other side.

When this valve assembly is used, all breathing must be done via the mouth, through the large mouthpiece shown attached to the valve assembly, and the nose must be clamped.  Facemask valve assemblies are available that allow breathing through both the mouth and the nose, and no mouthpiece is required.  No matter what type of breathing valve and apparatus are used, it is essential that air flow not be restricted, absolutely no air escape from the system, and the subject feel comfortable with the system.

 

 
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Overview of equipment (cont.)

Electronic gas analyzers.  Most systems for measuring VO2 use electronic oxygen and carbon dioxide analyzers, as shown.  These measure the percent oxygen and carbon dioxide, respectively, in a mixture of gases (usually expired air).  Many different models are available.  Electronic analyzers are usually the most expensive single item of equipment in the complete system, but they are easy to use, rapid, and accurate.  A small sample of gas is pulled through the analyzers by a vacuum pump, and the percent concentrations of oxygen and carbon dioxide are displayed on the digital meters (or can be read by a computer interfaced with the system).  Samples can be taken directly from the Collins gasometer or a Douglas bag, or expired air can be sampled continuously from a mixing chamber to give averaged gas concentrations over a period of time.  Samples are passed through a drying canister before entering the analyzers to remove all water from the sample.  This is done for two reasons: (a) To reduce the number of gases in the mixture to three, oxygen, carbon dioxide and nitrogen.  By doing this, only two of the gases have to be measured, and the third can be calculated as the remaining difference.  (b) To keep tubes from becoming clogged by moisture that condenses or by sediment in the moisture.

It is important to calibrate analyzers frequently using precision gas mixtures of known concentrations.  Calibration is the process of checking the accuracy of an instrument's measurements against some standard and, if possible, adjusting the instrument to measure accurately.  Electronic gas analyzers can be adjusted to precisely match precision calibration gases of known concentrations.

 

 
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Overview of Equipment (cont.)

Miscellaneous equipment.  Various additional small items of equipment are essential to complete the oxygen flow measurement system.  

(a) Large, low resistance hoses are used to connect various parts of the system, such as the nonrebreathing valve to the gasometer.

(b) Noseclips are used to prevent airflow through the nose when all air is to be breathed through the mouth.

(c) In order to standardize gas volumes to standard conditions (discussed later in the lab), the following are needed: a barometer for measuring atmospheric pressure, a thermometer for measuring the temperature of all gas volumes, a hygrometer for measuring relative humidity or amount of water vapor in a gas mixture.

(d) A headgear or other apparatus for supporting the nonrebreathing valve and connecting hose(s).

(e) Materials for cleaning and disinfecting  mouthpieces, valves and hoses.

 

 
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Measurement of Whole Body VO2

Oxygen is consumed by the body in aerobic metabolism.  In fact, oxygen is used and converted to water (by combining with hydrogen) in what may be considered the very last chemical reaction of the many reactions that make up aerobic metabolism.  The rate at which the entire series of reactions takes place is to a large extent dependent on the rate at which oxygen is converted to water, that is, consumed.  In the extreme case, if oxygen is not available for this last reaction, all of the reactions quickly stop, and ATP cannot be formed by aerobic metabolism.

We measure whole-body oxygen consumption by analyzing air breathed.  This is referred to as "pulmonary gas exchange" because it involves exchanging gases (i.e., oxygen and carbon dioxide) in the lungs.  Such pulmonary gas exchange measurements reflect aerobic metabolism in all cells of the body.  During vigorous exercise, oxygen consumed by exercising skeletal muscles dominates whole-body VO2.

 

 
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Measurement of whole-body VO2

VO2 may be described as the difference between the volume of oxygen breathed into the body (VIO2) and the volume of oxygen breathed out of the body (VEO2).  This can be summarized:

(1) VO2 = VIO2 - VEO2

In each minute, we take in a given volume of oxygen and exhale a smaller volume of oxygen.  The reason the volume of exhaled oxygen is less is because some oxygen was taken out of the air in the lungs, carried by the blood to cells throughout the body, and used (consumed) in aerobic metabolism.  Conceptually, then, measurement of VO2 is simple: Measure VIO2 and VEO2 and the difference is VO2.

 

 
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Measurement of whole-body VO2 (cont.)

To determine the volume of any gas in a mixture of gases, we multiply the total volume of the mixture by the fraction (the decimal form of the percent) made up by the gas of interest. For example, normal atmospheric air consists of 20.93% oxygen, 0.03% carbon dioxide, and 79.04% nitrogen. (Actually there are very small fractions of other gases, but in physiology these are lumped together with nitrogen because they are physiologically inert.) So, if we have a container that has 100 liters of air in it, we know that this container has 20.93 liters (100 L x 0.2093) of oxygen, 0.03 liters (100 L x 0.0003) of carbon dioxide, and 79.04 liters (100 L x 0.7904) of nitrogen.

 

 
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INLINE QUIZ LAB2Q1
 
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Measurement of whole-body VO2 (cont.)

The volume of oxygen inspired equals the total volume of air inspired (VI) multiplied by the fraction of oxygen in the inspired air (FIO2),and the volume of oxygen expired equals the total volume of air expired (VE) multiplied by the fraction of oxygen in the expired air (FEO2):

(2)   VIO2= V I x FIO2

(3)   VEO2 = VE x FEO2

If we substitute these expressions in Equation 1, VO2 may be calculated as:

(4)   VO2 = (VI x FIO2) – (VE x FEO2)

Remember that the fraction of oxygen in normal atmospheric air is a constant 0.2093. Therefore, as long as we are measuring VO2 while a person is breathing normal air, Equation 4 may be written:

(5)   VO2 = (VI x 0.2093) – (VE x FEO2)

This shows that we can determine VO2 by measuring three other variables: the total volume of air inspired (VI), the total volume of air expired during the same time period (VE), and the percent or fraction of oxygen in the air breathed out (FEO2).

 
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Measurement of whole-body VO2 (cont.)

The picture shows measurement of pulmonary gas exchange variables. The subject is inspiring through a dry gas meter, by which VI is determined, and expiring into a Collins gasometer, by which VE is determined. Let’s assume that VI =  48.3 L/min and VE = 46.9 L/min. Also, let’s assume that we analyzed the expired air in the gasometer and FEO2 = 0.1720. We can calculate this person’s VO2.

VO2 = (VI x 0.2093) – (VE x FEO2)

    = ([48.3 L/min] x 0.2093) – ([46.9 L/min] x 0.1720)
    = 2.0 L/min

Note that this person was taking in 10.1 L of oxygen per minute and breathing out 8.1 L of oxygen per minute.

 

 
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INLINE QUIZ
 
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Measurement of whole-body VO2 (cont.)

Although measurement of VO2 is really simple with measurement of both VI and VE, most laboratories use a system that measures only VI or VE. We still need to know both, and we can’t assume that they are the same (VI and VE are rarely equal). Fortunately, we can calculate one from the other. This is done by what is known as the Haldane transformation, as follows:

(6)   VI = (VE x FEN2) / FIN2

(7)   VE = (VI x FIN2) / FEN2

You can see that these conversions require knowledge of fractions of nitrogen (N2) in both the inspired air and the expired air. As long as we are measuring in normal atmospheric air, FIN2 = 0.7904. FEN2 must be determined. In most measurement systems, fractions of both oxygen and carbon dioxide are measured in expired air, and the remainder is known to be nitrogen (if the sample has been dried so no water vapor is in it).

 

 
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Measurement of whole-body VO2 (cont.) 

If we are measuring VO
2 in normal atmospheric air, after all
substitutions and algebraic simplifications are done, we end
up with the following equations. 

For calculating VO
2 when we measure minute volume of
ventilation on the inspired side: 

(8) VO
2 = VI x (0.2093 – [0.7904 x FEO2 / FEN2]) 

For calculating VO
2 when we measure minute volume of
ventilation on the expired side: 

(9) VO
2 = VE x ([0.2648 x FEN2] - FEO2

You can see that with either method of measuring VO
2, three
variables must be known: 

(a) F
EO2 – This is measured by running a sample of expired
air through an oxygen analyzer. 

(b) F
EN2 – This is most commonly determined by measuring
both FO
2 and FCO2 in a sample of expired air with gas
analyzers and taking the remainder as nitrogen (i.e., FN
2 =
1.00 – FO
2 – FCO2

(c) Either V
I or VE – This is measured with a dry gas meter, a Collins gasometer, an electronic flow meter, or another similar device.

 

 
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Measurement of whole-body VO2 (cont.)

Let's practice using these equations to calculate VO2.

EXAMPLE: This example uses values that are typical of a person at rest.

The expired gas from the person in this picture is collected in the Collins gasometer for 3 minutes. The measured volume of the expired gas (VE) is 20.5 liters. Electronic gas analyzers are used to sample the gas and determine the fractions of oxygen and carbon dioxide that make up the expired gas sample.

The analyzers read the fractions as 18.00% oxygen (FEO2 = 0.1800) and 2.30% CO2 (FECO2 = 0.0230). We want to calculate the oxygen this person consumed during this three-minute measurement period.

In order to calculate VO
2 using measured VE, we will use the equation

VO
2 = VE x ([ 0.2648 x FEN2] – FEO2)

In order to use this equation, we also need the fraction of nitrogen in the person’s expired air (F
EN2). Recall the fraction of nitrogen in expired air can be calculated by subtracting the fractions of oxygen and carbon dioxide in expired air from one.

F
EN2 = 1 – FEO2 – FECO2 

F
EN2 = 1 – 0.180 – 0.023 = 0.797

Substituting into our equation for VO
2, we find

VO
2 = 20.5 x ([0.2648 x 0.797] – 0.180)

VO
2 = 0.64 liters in this three-minute period, or 0.21 L/min.

 

 
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Measurement of whole-body VO2 (cont.)

EXAMPLE. This example uses values that are typical of a person doing exercise of moderate intensity.

The subject for whom VO2 was measured at rest in the previous example is now walking briskly on a motorized treadmill at a speed of 3.7 mph or about 16 min/mile. We will measure her VO2 during this bout by measuring the volume of inspired air over a one-minute period and measuring the gas fractions in her expired air during that same period.

VI as measured by the flowmeter during this minute was 22.00 liters of air. FEO2 was 0. 172 and FECO2 was 0.029, both measured by analysis of the subject’s expired air. Again we must calculate FEN2.

              FEN2 = 1 – FEO2 – FECO2.

              FEN2 = 1 - 0.172 – 0.029

              FEN2 = 0.799

(Eq. 8)   VO2 = VI x (0.2093 – [0.7904 x FEO2 / FEN2])    

              VO2 = 22.00 x (0.2093 – [0.7904 x 0.172 / 0.799])

              VO2 = 0.86 L 

Since 0.86 liter of oxygen was consumed in one minute, we can say the rate of oxygen consumption was 0.86 L/min.



 

 
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Measurement of whole-body VO2 (cont.)

EXAMPLE. This example uses values that are typical of a highly trained endurance athlete exercising at a high intensity, such that VO2max is elicited. Our subject is a male triathlete who had recently completed an ironman event. In this example he is running on a motorized treadmill at a speed of 268 meters per minute (6 minutes per mile) and up a positive 3% grade.

VE will be measured by collecting a 30 second sample of his expired air in the Collins gasometer. The gas fractions in this sample will then be measured by the electronic gas analyzers. The 30 second sample had the following values:

VE = 59.8 L

FEO2 = 0.166

FECO2 = 0.044

FEN2 = 1 – FEO2 – FECO2

FEN2 = 1 – 0.166 – 0.044

FEN2 = 0.790

VO2 = VE x ([0.2648 x FEN2] – FEO2)

VO2 = 59.8 x ([0.2648 x 0.790] – 0.166)

VO2 = 2.58 L

Since this sample duration was 30 seconds, his rate of oxygen consumption was 2.58 liters / 0.5 minutes or 5.15 L/min.

 

 
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inline quiz
 
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Measurement of whole-body VO2 (cont.)

VO2 is expressed in two types of units: either as the total, absolute volume of oxygen consumed per minute (i.e., L/min or mL/min), or as the relative volume of oxygen consumed adjusted for body weight (i.e., ml/kg/min). Both units are useful, depending on what we want to know. Sometimes we want to know the total volume of oxygen consumed, such as when we want to convert oxygen consumed to kilocalories of energy to determine the total caloric cost of a bout of exercise. In such cases, we use L/min or mL/min. But the total absolute volume of oxygen consumed is affected by body size. In general, a larger person will consume more oxygen because he/she has more cells. Remember, oxygen consumption takes place in individual cells in the body. So, when we want to eliminate the effect of body size, we express VO2 as ml/kg/min. One example is when we compare VO2 values of athletes in different sports. Often these athletes differ greatly in body size, so we eliminate the effect of body size on VO2 values to make comparison more valid and meaningful.

It is essential that you be proficient at converting between L/min and mL/kg/min. This is done as follows.

To convert L/min to mL/kg/min:

     mL/kg/min = (L/min) x 1000 / body weight in kilograms

To convert mL/kg/min to L/min:

     L/min = (mL/kg/min) x body weight in kilograms / 1000

(Remember that weight in kilograms = weight in pounds / 2.205)

 

 
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Measurement of whole-body VO2 (cont.)

CALCULATION EXAMPLE 1: Suppose the triathlete on Page 22 has a body weight of 75 kg. To find his relative VO2 in ml/kg/min, we divide his absolute VO2 of 5.15 L/min by his body weight in kilograms, then multiply by 1000. 

Relative VO2 = (5.15 L/min / 75 kg) x 1000 ml/L

Relative VO2 = 68.7 ml/kg/min

CALCULATION EXAMPLE 2: Suppose an oarsman paddling a skull has a relative VO2 of 28.5 ml/kg/min. If his body weight is 200 lb, find his absolute VO2 in liters per minute.

First, we will convert 200 lb to kg:  200 / 2.205 = 90.7 kg.

Absolute VO2 = (relative VO2 x body weight in kg) / 1000

Absolute VO2 = (28.5 x 90.7) / 1000

Absolute VO2 = 2.59 L/min

 

 
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Measurement of whole-body VO2 (cont.)

CALCULATION EXAMPLE 3: While running on a treadmill, a runner who weighs 70 kg. has his inspired air flow rate measured. To calculate his relative VO
2 during this bout, his expired gas was concurrently analyzed for fractional content of O2 and CO2. The measurements were as follows: 

VI = 57.3 L/min

FEO2 = 0.155

FECO2 = 0.049

We wish to calculate his absolute and relative VO2.

FEN2 = 1 - 0.155 – 0.049

FEN2 = 0.796

Absolute VO2 = VI x (0.2093 – [0.7904 x FEO2 / FEN2])

Absolute VO2 = 57.3 x (0.2093 – [0.7904 x 0.155 / 0.796])

Absolute VO2 = 3.18 L/min

Relative VO2 = (3.18 L/min / 70 kg) x 1000 ml/L

Relative VO2 = 45.5 ml/kg/min

 
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inline quiz
 
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Measurement of Whole-Body VCO2

VCO
2 is the volume of carbon dioxide produced and expired by the body, usually expressed per minute. Although usually VO2 is of primary concern, often VCO2 is important to know also. It is easily calculated from the same measurements that are done to determine VO2. Conceptually, VCO2 is the difference between amount of CO2 expired and the amount inspired. Note that this is the opposite of oxygen, though the concept is the same. With oxygen, we take in a relatively large amount, consume some, and expire a smaller amount.  With carbon dioxide, we take in a small amount (usually close to none, because there is so little CO2 in normal air), we produce CO2 in metabolism and other chemical reactions in body cells, and we breathe out a larger amount than taken in. So:

(10) VCO2 = VECO2 – VICO2

The final equations that are used to calculate VCO2 in most measurement systems are as follows:

For calculating VCO2 when we measure minute volume of ventilation on the inspired side:

(11) VCO2 = VI x ([0.7903 x FECO2 / FEN2] – 0.0003)

For calculating VCO2 when we measure minute volume of ventilation on the expired side:

(12) VCO2 = VE x (FECO2 – [FEN2 x 0.0004])

VCO2 is almost always presented in units of L/min or ml/min and almost never as ml/kg/min (as VO2 often is).

 

 
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Measurement of Whole-Body VCO2 (cont.)

EXAMPLE 1: In a 30 second period, a person has an expired volume of 38 L. Analysis of the expired gas shows

FEO2 = 0.171
F
ECO2 = 0.043

To calculate VCO2 in this example, first we must calculate FEN2. Recall that

FEN2 = 1 - FEO2 - FECO2

FEN2 = 1 - 0.171 - 0.043
F
EN2 = 0.786

VCO2 = VE x (FECO2 - [FEN2 x 0.0004])
VCO
2 = 38 x (0.043 - [0.786 x 0.0004])

VCO2 = 1.62 L in the 30-second period.

EXAMPLE 2: Suppose the same subject is performing the same exercise but the inspired air flow rate is being measured and gas fractions are being measured in expired air. VI = 75.6 L/min. We can calculate VCO2 in this case.

FEO2 = 0.171

FECO2 = 0.043

FEN2 = 1 - 0.171 - 0.043
F
EN2 = 0.786

VCO2 = VI x ([0.7903 x FECO2 / FEN2] - 0.0003)
VCO
2 = 75.6 x ([0.7903 x 0.043 / 0.786] - 0.0003)

VCO
2 = 3.25 L/min

 

 
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inline quiz
 
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Standardization of Gas Volumes (STPD Conditions)

It is common practice in exercise physiology to correct VO2 and VCO2 values to a set of standard conditions known as STPD conditions. STPD stands for “standard temperature, pressure, dry.” The reason for this is that the volume of any gas is affected by the atmospheric pressure “pressing in on it,” its temperature, and the amount of water vapor in the sample. Let’s assume, for example, that we put 100 liters of air in a Douglas bag in the lab at The University of Texas at Tyler. If we would take this bag to Denver, the “mile-high city,” the gas would expand so there would be more than 100 liters in the bag, because of a lower atmospheric pressure at the higher altitude. If we would take the bag to Death Valley, the volume would shrink to less than 100 L, because of a greater atmospheric pressure pressing on the bag. Also, let’s assume the temperature of the gas was 20 degrees Celsius when we originally put the 100 L in the bag. If the temperature were 0 degrees when we take the bag to Denver, that would make the volume shrink; if the temperature were 40 degrees in Death Valley, that would make the volume expand. Finally, if we would take all the water vapor out of the original 100-L sample, the volume would be reduced; if we saturated the sample so it held all the water vapor it possible could, the volume would increase.

In short, it would be very difficult to compare measurements made under different conditions, especially conditions of different altitude and pressure, as well as temperature. Therefore, physiologists measure the ambient conditions of barometric pressure, and the temperature and vapor pressure of gas samples; these are referred to as ATPS conditions (ambient temperature, pressure and saturation). They then correct measured volumes to STPD conditions. This allows valid comparisons of VO2 and VCO2 values measured under all conditions, including measurements of skiers at an altitude of 12,000 feet, divers 50 feet below sea level, runners competing in the desert heat of Death Valley, and sledders in the Arctic.

Calculations of correction factors to standardize gas volumes to STPD conditions are easy to do, but we will not do these in this course. It is important, however, that you know that this correction is essential and that it is standard practice. You will usually see in research literature reports of “VO2 (STPD).” It is also important that you realize that measurement of VO2 requires determination of barometric pressure and the temperature and vapor pressure of any gas volume that is measured.

 

 
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Computerized Measurement Systems

In this lab you have been introduced to the fundamentals of measuring whole-body VO2 and VCO2 by pulmonary gas exchange. I hope you can see that the underlying concepts and the basic, manual procedures are straightforward and not difficult. And measurements can be very accurate if technicians are trained and pay attention to detail. Of course, a certain amount of rather expensive equipment is needed to make these measurements, especially the gas analyzers. The techniques I have described in this lab and the calculations involved are labor-intensive, however, and subject to technician error. So, most laboratories use computerized, automated systems for these measurements. Computerized systems allow essentially unlimited samples to be measured in succession, with rapid calculations of data and instantaneous feedback. Also, they require little technician involvement. They are not necessarily or automatically accurate, however. These instruments must be calibrated to assure that they are accurate and stable. And of course, these automated systems cost more.

Most of the computerized systems are based on the concepts and calculations we have dealt with in this lab. If you have the opportunity to work with such a system, the knowledge you have gained from this lab will help you understand “where the measurements are coming from.” 

 

 
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Lab Assignment

Using the formulas presented in this lab, make the following calculations.

1.   While riding a stationary bicycle ergometer, the following steady-state values were obtained on a subject whose body weight was 74 kg:

  • VI = 40.16 L/min
  • FEO2 = 0.168
  • FECO2 = 0.047

Based on this information, calculate this subject's steady-state

  • (a) absolute VO2 in L/min
  • (b) relative VO2 in ml/kg/min
  • (c) VCO2 in L/min

 

2.   While performing arm-crank ergometry, a patient's expired air was collected in a Douglas bag.  The collection period was 40 seconds and the patient's weight was 85 kg.  The following values were obtained on the air in the Douglas bag:

  • V = 12.0 L
  • FEO2 = 0.171
  • FECO2 = 0.036

Based on this data for this 40-second period, calculate the subject's

  • (a) VE in L/min
  • (b) absolute VO2 in L/min
  • (c) relative VO2 in ml/kg/min
  • (d) VCO2 in L/min

 

Submit the problems and their solutions to the instructor via attachment to email.  The attachment should include

  • The problem restated as it appears on this page
  • All formulas used in its solution
  • All formulas with appropriate values substituted into
     the formulas
  • The values asked for in the problem

In short, your solutions to the problems should look like the solutions to example problems presented in this lab.  The subject line of the email used to submit this assignment should be "your name-lab 2".

This concludes Lab 2.

 

 
 
Lesson: Lab 3 - Oxygen Consumption in Response to Acute Exercise 3 Lab 3 - Oxygen Consumption in Response to Acute Exercise Edit this lesson (Lab 3 - Oxygen Consumption in Response to Acute Exercise)
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Introduction

The focus of Lab 3 is VO2 response to acute submaximal and maximal exercise. In Lab 2, you learned the mechanics of VO2 measurement. In Lab 3 you will observe and analyze VO2 measurements made on two subjects during various bouts of exercise.     

NOTE:  In this lab you will notice an additional button in the left-hand navigation bar.  The "more info" button will become active as you view pages 23 and 27 of this lab.  Clicking the "more info" button will display a page containing information pertinent to the activities being described on pages 33 and 38. 

Learning Objectives

After completion of this lab, the student should be able to:

1. Describe the response of VO2 to an acute bout of exercise, both at intensities below VO2max and at intensities above VO2max. This description should include the concepts of:

· oxygen demand 
· oxygen deficit 
· steady-state VO
2 
· excess post-exercise oxygen consumption 
· distinguishing between responses of individuals of
  different sizes and fitness levels to exercise of various
  types.

2. Describe the relationship between VO2 and exercise intensity or power output, including the concept of VO2max.

3. Describe the general protocol that is used for measuring VO2max.

 
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Instrumentation

This lab will utilize much of the equipment and instrumentation described in Lab 2.  Included will be:

  • A Monark bicycle ergometer for measuring rate of doing work or power output.

  • A motorized treadmill for running.

  • A Collins gasometer for measuring VE.

  • A dry gas meter for measuring VI.

  • A mixing chamber for continuous sampling of expired gas.

  • A nonrebreathing valve assembly for controlling direction of gas flow during inhaling and exhaling.

  • A nose clip for pinching off the nose so that all gases inhaled and exhaled must pass through the nonrebreathing valve.

  • Hoses to connect the nonrebreathing valve to the gasometer, dry gas meter, and mixing chamber.

  • Electronic gas analyzers for measuring O2 and CO2 fractions.

  • Calibration gas of known composition to confirm the accuracy of the electronic gas analyzers’ readings.

  • A drying tube to remove moisture from expired gas prior to its entry into the electronic gas analyzers.

  • A barometer to measure atmospheric pressure.

  • Thermometers to measure ambient atmospheric temperature and gas sample temperature.

  • Hygrometer to measure relative humidity in the ambient air.

  • Materials for cleaning and disinfecting mouthpieces, valves and hoses.

  • PC and software to correct ambient conditions to STPD and calculate VO2 from measurements acquired.

 

 
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Overview

In the pictures shown here, each subject is seated on a Monark bicycle ergometer. Each subject is outfitted with a nonrebreathing valve, headgear and nose clip.  The subjects' inspired air is being drawn through a dry gas meter and their expired air is being sampled by electronic gas analyzers.  This configuration allows measurement of VI, FEO2 and FECO2.  The dry gas meter and gas analyzers are interfaced with a computer so that VO2 is automatically calculated for each consecutive 30-second interval.

The subject on the left (Subject 1) is a 48-year-old male who weighs 162 lb (74 kg); the subject pictured on the right (Subject 2) is a 28-year-old female who weighs 119 lb (54 kg).  Both subjects are healthy and active.  Both are recreational runners who also do some weight lifting.

One or both subjects will have VO2 measured while doing the following exercise bouts:

I.  VO2 Response to Continuous Submaximal Exercise

  • Pedaling the Monark bike ergometer continuously for 10 minutes    at an external power output of 300 kgm/min.  (p. 4-11)

  • Pedaling the Monark bike ergometer continuously for 10 minutes at an external power output of 300 kgm/min.  (p. 12-13)  

II. Pedaling the Monark bike ergometer continuously for 9 minutes at an external power output of 300 kgm/min during minutes 1-3, 600 kgm/min during minutes 4-6 and 900 kgm/min during minutes 7-9. (p. 14-16)

III. A series of 3-minute runs on a treadmill.  The runs will be submaximal initially and become progressively more intense until VO2 max is attained.   (p. 17-27)

IV.  A 3-minute bout of arm cranking at an external power output of 300 kgm/minute. (p. 28)

 
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I. VO2 Response to Continuous Submaximal Exercise

Cycling at 300 kgm/min

In our first demonstration both subjects cycle continuously for 10 minutes at an external power output of 300 kgm/min.  VO2 is measured prior to, during and immediately following the 10-minute bout of cycling.   To accomplish this, average VO2 is measured for each consecutive 30-second interval during a 20-minute period.  The 20-minute VO2 measurement period is divided into the following segments:

Minutes 1-3: Pre-exercise or resting VO2 is measured.  The subjects are seated on the stationary bicycles but they are not pedaling.

Minutes 4-13: Exercise VO2 is measured.  This is the 10-minute exercise period during which the subject is pedaling.

Minutes 14-20: immediate post-exercise VO2 is measured.  The subjects stop pedaling after minute 13 but remain seated on the stationary bike for the remaining 7 minutes. 

 
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I. VO2 Response to Continuous Submaximal Exercise

Cycling at 300 kgm/min (cont.)

The following charts show VO2 for each of the subjects during Minutes 1-3 (the 3-minute period immediately pre-exercise):

The chart on the top is for Subject 1, the 74 kg male and the lower chart is for Subject 2, the 54 kg female.  Notice that his average resting VO2 is 0.38 L/min and her average resting VO2 is 0.25 L/min.  Recall from Lab 2 that one determinant of absolute VO2 is body size.  A person with a larger body size and body weight can be expected to have a greater resting VO2 than a person of lesser size and weight.

Let's calculate relative VO2 at rest for each subject.

For Subject 1:
     relative VO2 at rest = 0.38 L/min x 1000 / 74 kg
     relative VO
2 at rest = 5.1 ml/kg/min

For Subject 2:
     relative VO
2 at rest = 0.25 L/min x 1000 / 54 kg
     relative VO
2 at rest = 4.6 ml/kg/min

Notice that although the two subjects exhibit different absolute resting VO2, relative VO2 values at rest are similar.

 

 
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I. VO2 Response to Continuous Submaximal Exercise

Cycling at 300 kgm/min (cont.)

Another unit used to express rate of oxygen consumption is the MET or metabolic equivalent.  One MET is equal to a relative VO2 of 3.5 ml/kg/min.  Resting VO2 in adults averages 1 MET or 3.5 ml/kg/min.  3.5 ml/kg/min or 1 MET is the mean resting VO2 value for the adult population, resting VO2 may vary between individuals.  Not all persons have resting VO2 values of exactly 3.5 ml/kg/min, nor does an individual have the same resting VO2 at all times. 

The MET unit can also be used to express exercise VO2.  For instance, if a person has a relative VO2 of 35 ml/kg/min during exercise, he or she is said to have a VO2 of 10 METS (35/3.5).

 
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I. VO2 Response to Continuous Submaximal Exercise

Cycling at 300 kgm/min (cont.)

Three minutes into the 20-minute measurement period, the subjects begin their 10-minute bouts of cycling at 300 kgm/min. 

The charts below show VO2 measured during Minutes 1-4 (pre-exercise and the first minute of exercise).

Note that at the start of exercise, average VO2 = 0.38 L/min for Subject 1 and 0.25 L/min for Subject 2 (their resting VO2 values).  After the onset of exercise VO2 increased during the first minute of exercise, reaching average values of 0.81 L/min for Subject 1 and 0.74 L/min for Subject 2 during the 3:30-4:00 interval.  The rate of doing external work, however, abruptly increased from 0 to 300 kgm/min at the onset of exercise and remained constant throughout the entire 10-minute exercise bout.  Note that the rate of doing external work can increase much more quickly than VO2 can increase in response to energy demand.

 

 
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I. VO2 Response to Continuous Submaximal Exercise

Cycling at 300 kgm/min (cont.)

The next 2 charts depict VO2 for Minutes 1-5.

VO2 for Subject 1 is now 1.03 L/min and VO2 for Subject 2 is 0.94 L/min during the second minute of exercise.  Although VO2 is still rising, it is not rising as fast as it did during the first minute of exercise. 

 

 
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I. VO2 Response to Continuous Submaximal Exercise

Cycling at 300 kgm/min (cont.)

The charts below depict VO2 vs. time for the first 13 minutes of the 20-minute measurement period (pre-exercise through Minute 10 of the exercise bout).  Notice that VO2 varies very little for either subject during Minutes 6-13 on the charts (Minutes 3-10 of exercise). 

Assuming that cycling at 300 kgm/min is submaximal for both of these subjects, VO2 during Minutes 3-10 of exercise is said to be steady-state; that is VO2 is essentially constant (with some small variation but not large enough to be of consequence).   Steady-state VO2 is adequate to enable oxidative metabolism to supply the energy required by the exercise.  During this bout, steady-state VO2 for Subject 1 averages 1.05 L/min and for Subject 2 steady-state VO2 averages 0.98 L/min (average for Minutes 3-10 of exercise).  Confirmation that 1.05 L/min and 0.98 L/min are submaximal VO2 values for these subjects is presented later in this lab when VO2 values increase while cycling at 600 kgm/min.  We say the oxygen demand (O2 demand) of pedaling the Monark bicycle ergometer at 300 kgm/min is 1.05 L/min for Subject 1 and 0.98 L/min for Subject 2 (their steady-state VO2 over minutes 3-10 of exercise).

Notice that during the first 2 minutes of exercise, VO2 was less than the steady-state value achieved during minutes 3-10 of exercise.  Any time VO2 is less than O2 demand during exercise, this is referred to as O2 deficit.  There is always an O2 deficit when the power output increases abruptly.  There is additional O2 deficit during high intensity exercise when VO2 = VO2 max and O2 demand exceeds VO2 max.

 

 
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I. VO2 Response to Continuous Submaximal Exercise

Cycling at 300 kgm/min (cont.)

Note that steady-state absolute VO2 was essentially the same for both subjects as they both performed external work at the same rate.  The slight difference (1.05 L/min vs. 0.98 L/min) may be accounted for by 2 factors.  Recall that Subject 1, having a higher body weight and size than Subject 2 had a higher resting absolute VO2. In addition, Subject 1 could be performing more internal work to move his heavier lower limbs in the pedaling motion.

Subject 2 has a higher steady-state relative VO2 than Subject 1, however.

For Subject 1 -  relative VO2 = (1.05 L/min x 1000) / 74kg
                           relative VO
2 = 14.2 ml/kg/min

For Subject 2 -  relative VO2 = (0.98 L/min x 1000) / 54kg
                           relative VO
2 = 18.2 ml/kg/min

The same rate of work is relatively more costly for the smaller person.

 

 
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I. VO2 Response to Continuous Submaximal Exercise

Cycling at 300 kgm/min (cont.)

After 10 minutes of exercise (at the 13-minute point) the subjects stop pedaling.  How do you expect their VO2 to change when they stop?  Will it immediately return to pre-exercise value? Let’s study the charts again, this time during the 7 minutes immediately post-exercise (Minutes 14-20  on the charts).

Notice VO2 does not immediately return to pre-exercise value for either subject.  During the first minute post-exercise, Subject 1 still exhibits a VO2 of 0.59 L/min and Subject 2’s VO2 is 0.54 L/min.  In the second minute post-exercise neither subject’s VO2 has returned to pre-exercise value (0.41 L/min for Subject 1 and 0.38 L/min for Subject 2).  Further examination of the charts reveals that VO2 does not return to pre-exercise value until 4:30-5:00 post-exercise for Subject 1 and 5:30-6:00 post-exercise for Subject 2.  Note that during this immediate post-exercise period, VO2 exceeds the resting or pre-exercise rate.  This is  Excess Post-Exercise Oxygen Consumption (recall the discussion of EPOC from Unit 2 Lesson 3).

 

 
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I. VO2 Response to Continuous Submaximal Exercise

Cycling at 600 kgm/min

After a rest period, another 20-minute period begins during which both subjects will have their average VO2 measured during each consecutive 30-second interval.  As in bout 1,  the subjects will be resting on the Monark bicycle ergometer during Minutes 1-3.  During Minutes 4-13 the subjects will be pedaling and during Minutes 14-20 the subjects will again be resting on the stationary bike.  In this exercise bout, however, the external power output will be 600 kgm/min.  

 

 
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I. VO2 Response to Continuous Submaximal Exercise

Cycling at 600 kgm/min (cont.)  

The charts shown above depict VO2 vs. time for both subjects during the 20-minute period that includes the 10-minute bout of cycling at 600 kgm/min.

As Part 1 of your lab assignment, answer the following questions and include them in an email attachment along with the other questions appearing later in this lab.

1.    The chart depicting Subject 1's VO2 vs. time at 600 kgm/min is divided into 5 areas; A,B,C,D and E. 

  • Which area represents steady-state exercise VO2?

  • Which area represents the period of EPOC?

  • Which area represents the period of oxygen deficit?

  • Which area represents pre-exercise VO2?

  • Which area represents return to resting VO2 after exercise?

2.     What is the approximate steady-state VO2 of Subject 1 while cycling at 600 kgm/min expressed in absolute terms?

3.     What is the approximate steady-state VO2 of Subject 2 while cycling at 600 kgm/min expressed in absolute terms?

4.     What is the approximate steady-state VO2 of Subject 1 while cycling at 600 kgm/min expressed in relative terms?

5.     What is the approximate steady-state VO2 of Subject 2 while cycling at 600 kgm/min expressed in relative terms?

6.     Approximately how long did the period of EPOC last for Subject 1?

7.     Approximately how long did it take for Subject 1 to reach steady-state VO2 after the onset of exercise?

8.     Was the relative work rate during this bout greater for Subject 1 or Subject 2?

 

 
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II. VO2 Response to Progressive Exercise  

The next exercise bout is performed only by Subject 1.  The exercise bout is a 9-minute bout of pedaling the Monark bicycle ergometer and is subdivided as follows:
  • During Minutes 1-3 the subject cycles at 300 kgm/min
  • During Minutes 4-6 the subject cycles at 600 kgm/min
  • During Minutes 7-9 the subject cycles at 900 kgm/min

The VO2 measurement period is 18 minutes with exercise beginning 3 minutes after VO2 measurement is initiated.  The VO2 measurement period is divided as follows:

  • Minutes 1-3 the subject is resting while seated on the Monark bicycle egometer  (pre-exercise).
  • Minutes 4-6 the subject is cycling at 300 kgm/min.
  • Minutes 7-9 the subject is cycling at 600 kgm/min.
  • Minutes 9-12 the subject is cycling at 900 kgm/min.
  • Minutes 13-18 the subject is resting while seated on the Monark bicycle ergometer (post-exercise recovery).

 

 
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II. VO2 Response to Progressive Exercise (cont.)

After resting VO2 is measured for 3 minutes, Subject 1 begins cycling at a power output of 300 kgm/min (exercise begins at the start of Minute 4).  Subject 1 pedals the bike at 300 kgm/min for 3 minutes. 

At the start of Minute 7, power output is increased to 600 kgm/min.  The subject cycles at 600 kgm/min for 3 minutes (Minutes 7-9).

At the start of Minute 10, power output increases again to 900 kgm/min.  The subject cycles at 900 kgm/min for 3 minutes (Minutes 10-12).

During Minutes 13-18 VO2 is measured during recovery.

 
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II. VO2 Response to Progressive Exercise (cont.)

The following chart depicts VO2 during the bout of cycling at progressively increasing work rate.

Lab Assignment - Part 2.  Study the chart and answer the following questions:

  • What is the subject's steady-state VO2 while cycling at 300 kgm/min?
  • What is the subject's steady-state VO2 while cycling at 600 kgm/min?
  • What is the subject's steady-state VO2 while cycling at 900 kgm/min?
  • The work rate is abruptly increased from 600 to 900 kgm/min at the end of Minute 9.  Approximately how long does it take for VO2 to go from steady-state for 600 kgm/min to steady-state for 900 kgm/min?
  • At what periods during this bout was O2 deficit exhibited?
  • Was VO2 max reached during cycling at 600 kgm/min?  Why or why not?
  • Was VO2 max reached during cycling at 900 kgm/min?  Why or why not?

 

 
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III. VO2 max Testing

Next, we will conduct tests to determine the maximal oxygen consumption or VO2 max of both subjects.  Recall that VO2 max is the maximum rate at which the body can transport and utilize oxygen.  VO2 can be measured during exercise in a variety of modes (running, biking, swimming, cranking with the arms, etc.).  There is a maximum VO2 an individual can attain in any given exercise mode, but VO2 max is the highest VO2 attainable in any mode.  The highest VO2 attainable in a given mode of exercise is referred to as VO2 peak if it is less than that person’s VO2 max.  VO2 peak varies with exercise mode due to differences in muscle mass involved in the exercise and with state of training.  In general, higher oxygen uptakes can be attained during exercises that involve more and larger muscle groups.  Running on a treadmill is the most appropriate VO2 max testing mode for most subjects because running involves large muscle groups and the muscles involved in locomotion are involved in regular daily activity.  Running on a treadmill will be the exercise mode used in this test.

Let's consider a triathlete example to help clarify the difference between VO2 peak and VO2 max:

  • Max attainable VO2 in swimming - 45 ml/kg/min

  • Max attainable VO2 in biking - 51 ml/kg/min

  • Max attainable VO2 in running - 60 ml/kg/min

The VO2 values attained in swimming and biking were VO2 peak values and the VO2 value attained in running is this athlete's VO2 max.

In trained athletes maximum VO2 measurements should be obtained in the mode they have trained for (such as a trained cyclist or swimmer).  The muscle groups that are directly involved in the activity such athletes train for have highly developed oxidative capacity and may be capable of utilizing oxygen at a higher rate than larger muscle groups that are not so highly trained.  Testing of athletes should be sport-specific, and a VO2 peak value in the athlete’s sport is usually the most meaningful measurement in terms of performance. 

 
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III. VO2 max Testing (cont.)

The testing protocol used in this lab consists of a series of 3-minute running bouts on a treadmill as follows:

A. The first 3-minute bout is of sufficiently low intensity so that the O2 demand is submaximal; that is O2 demand is below the subject’s VO2 max (usually done at  0% grade and at a comfortable running speed).  VO2 is measured during the last 30 seconds of the bout, allowing VO2 to reach steady-state during the first 2 minutes of the bout.

B. After a rest period, another 3-minute bout is performed with the treadmill grade increased slightly.  Uphill running at any given speed has a higher O2 demand than running on a level treadmill at that given speed.  Again, VO2 is measured during the final 30 seconds of this bout, the expectation being that VO2 will increase in response to the increase in O2 demand.  If VO2 does increase, subsequent bouts are performed at ever-increasing intensity (increasing grade or speed) until a bout is performed in which VO2 fails to rise in response to the increase in O2 demand.  The highest VO2 attained during this series of running bouts is VO2 max.  

     (Actually, the highest VO2 attained in this protocol is a VO2 peak, but since neither subject is highly trained in any other endurance sport and since running involves a larger amount of muscle mass than other modes of exercise they could perform, it is safe to assume that VO2 peak reached in this running protocol is VO2 max.) 

 
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III. VO2 max Testing (cont.)

In this picture, Subject 1 is performing his first 3-minute bout of treadmill running. 

Speed = 214 m/min
Grade = 0% (Level treadmill)

During the final 30 seconds of the run, his expired air is collected in the Collins gasometer.  Analysis of VE and expired gas fractions show his VO2 during this 30-second period is 3.00 L/min or 40.6 ml/kg/min

 

 
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III. VO2 max Testing (cont.)

After a short rest, Subject 1 performs his next 3-minute bout.

Speed = 214 m/min
Grade = +2.5%

During the final 30 seconds of the bout, his expired air is again collected in the Collins gasometer.  Analysis of VE, FEO2 and FECO2 showed his VO2 for this stage is 3.36 L/min or 45.4 ml/kg/min.

 

 
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III. VO2 max Testing (cont.)

After another rest period, Subject 1 performs another 3-minute bout. 

Speed = 214 m/min
Grade = +5%

Analysis of his expired air shows his VO2 for the final 30 seconds of this third stage is 3.95 L/min or 53.4 ml/kg/min.

 

 
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III. VO2 max Testing (cont.)

Since the subject’s VO2 in Bout 3 increases over his VO2 in Bout 2, we know VO2 max was not reached in Bout 2.   We do not know if VO2 max is reached in Bout 3 so another bout is required.  After another rest period, Subject 1 performs another 3-minute bout.

Speed = 214 m/min
Grade = 7.5%

Analysis of his expired air during the final 30 seconds of Bout 4 shows his VO2 is 3.97 L/min or 53.7 ml/kg/min, only slightly higher than his VO2 for the previous bout.  The failure of the subject’s VO2 to rise in response to the increased O2 demand in Bout 4 indicates VO2 max has been attained.  The chart below shows VO2 at each bout.  Notice the VO2 curve becomes essentially flat at Bout 3.

VO2 max is the highest VO2 attained during any bout of this test.  Subject 1’s VO2 max is 3.97 L/min, 53.7 ml/kg/min, or 15.3 METs.

  

 
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III. VO2 max Testing (cont.)

VO2 max values vary greatly between different individuals.  VO2 max may be as low as 10-15 ml/kg/min in persons suffering from heart disease to 80 ml/kg/min in elite endurance athletes.  Normative data from the Cooper Institute and from the American Heart Association is presented in the “more info” page (click button on navigation bar):

Comparison of Subject 1's VO2 max to subjects of the same age and gender in Cooper Institute data shows Subject 1’s VO2 max is between the 95th and 99th percentile.

 


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Cooper Institute Data for VO2 max (ml/kg/min) in Men by Age Groups (yrs)
 
%ile 20-29 30-39 40-49 50-59 60+

99 58.79 58.86 55.42 52.53 50.39
95 53.97 52.53 50.36 47.11 45.21
90 51.35 50.36 48.20 45.31 42.46
85 49.64 48.20 45.31 42.42 39.53
80 48.20 46.75 44.11 40.98 38.09
75 46.99 45.31 43.89 39.53 36.65
70 46.75 44.59 41.75 38.45 35.30
65 45.31 43.87 40.98 37.61 39.29
60 44.23 42.42 39.89 36.65 33.59
55 43.87 41.58 39.53 36.10 32.39
50 42.49 40.98 38.09 35.20 31.83
45 42.42 39.53 37.37 34.12 30.87
40 40.98 38.86 36.69 33.76 30.15
35 40.26 38.09 35.56 32.48 29.43
30 39.53 37.37 35.13 32.31 28.70
25 38.09 36.65 33.76 31.06 27.89
20 37.13 35.35 33.04 30.15 26.54
15 36.65 34.0 32.31 29.43 25.09
10 34.48 32.53 30.85 27.98 23.05
5 31.57 30.87 28.29 25.09 20.76
1 27.09 26.54 24.15 22.06 18.28

American Heart Association Data for VO2 max in ml/kg/min for Men by Age (yrs.)

Age VO2 max

20-29 43 + 7.2
30-39 42 + 7.0
40-49 40 + 7.2
50-59 36 + 7.1
60-69 33 + 7.3
70-79 29 + 7.3
 
 
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III. VO2 max Testing (cont.)

Subject 2 now begins her VO2 max test.  Her test protocol is the same as Subject 1’s protocol, intermittent stages consisting of 3-minute treadmill running bouts at progressively increasing intensity with VO2 being measured during the final 30 seconds of each bout.  Subject 2 performs her first bout.

Speed = 187 m/min
Grade = 0%

Analysis of her expired air during the final 30 seconds of Bout 1 shows that her VO2 is 2.13 L/min or 39.5 ml/kg/min.

 

 
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III. VO2 max Testing (cont.)

After a short rest, Subject 2 performs her next bout.  The intensity (and O2 demand) of Bout 2 is greater than in Bout 1.  The increase in intensity is accomplished by increasing the speed of the treadmill. 

Speed = 214 m/min
Grade = 0%

Analysis of her expired air during the final 30 seconds of Bout 2 shows her VO2 was 2.23 L/min or 41.2 ml/kg/min. Notice that Subject 2's relative VO2 of 41.2 ml/kg/min is similar to Subject 1's relative VO2 (40.6 ml/kg/min) at this same speed and 0% grade.

 
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III. VO2 max Testing (cont.)

After a rest period, Subject 2 performs her third bout.

Speed = 214 m/min
Grade = 2.5%

 

Analysis of her expired air during the final 30 seconds of Bout 3 reveals that her VO2 = 2.37 L/min or 43.9 ml/kg/min.

 
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III. VO2 max Testing (cont.)

After a rest period, Subject 2 performs her fourth bout.

Speed = 214 m/min
Grade = 5.0%

Analysis of her expired air during the final 30 seconds of this bout shows her VO2 for this bout is 2.38 L/min or 44.0 ml/kg/min. 

Part 3 of your lab assignment is to determine:

  • Whether or not Subject 2 must perform another bout to determine or verify VO2 max and why.

  • What is Subject 2's VO2 max?  Express her VO2 max in absolute units, relative units and METS.

  • Using the "more info" button, determine how her VO2 max compares with others of her age and gender by the Cooper Institute data.

 

 


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Cooper Institute Data for VO2 max (ml/kg/min)  in Women by Age Groups (yrs)

%ile 20 - 29 30 - 39 40 - 49 50 - 59 60 +

99 53.03 48.73 46.75 42.04 44.47
95 46.75 43.87 40.98 36.81 37.46
90 44.15 40.98 39.53 35.20 35.20
85 42.42 40.26 37.49 33.59 32.31
80 40.98 38.57 36.28 32.31 31.23
75 39.53 37.37 35.11 39.90 30.87
70 38.09 36.65 33.76 30.87 29.43
65 37.37 35.44 33.04 29.76 27.98
60 36.65 34.60 32.31 29.43 27.21
55 36.14 33.85 31.59 28.70 26.54
50 35.20 33.76 30.87 28.22 25.82
45 34.48 32.41 30.58 27.98 25.09
40 33.76 32.31 29.45 26.85 24.49
35 32.72 31.09 29.43 26.13 24.03
30 32.31 30.51 28.25 25.48 23.80
25 30.94 39.93 27.98 25.09 23.65
20 30.63 28.70 26.54 24.25 22.78
15 29.43 27.98 25.57 23.65 22.21
10 28.39 26.54 25.09 22.33 20.76
5 25.89 25.09 23.53 21.10 19.68
1 22.57 22.49 20.76 18.74 17.87

American Heart Association Data for VO2 max in ml/kg/min for Women by Age (yrs.)

Age VO2 max

20-29 36 + 6.9
30-39 34 + 6.2
40-49 32 + 6.2
50-59 29 + 5.4
60-69 27 + 4.7
70-79 27 + 5.8
 
 
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IV. VO2 During Arm Cranking

The final section of this lab involves VO2 measurement during arm cranking at an external work rate of 300 kgm/min (note that this external work rate is the same as in bout 1 of cycling).  VO2 is measured every 30 seconds during a 3-minute cranking bout.  The chart below shows Subject 1’s VO2 vs. time during the 3-minute cranking bout.   

Notice the steady-state VO2 reached during the final minute of the bout is 1.23 L/min, a higher value than that attained in cycling with the legs at the same external work rate (1.05 L/min).  During arm cranking or during most other upper body exercise, the muscles of the pelvis, trunk and shoulder girdle must contract to stabilize the body (maintain posture) and hold the body in position while force is being exerted by the hands.  For this reason, exercise with the upper body tends to have a higher O2 demand for a given external work rate than does exercise with the lower body.  If the upper body exercise does not require posture maintenance,  VO2 for a given work rate more closely matches that for lower body exercise.   Also, VO2 peak measured during upper body exercise is 20-30% lower than when measured during lower body exercise in the same person, probably due to smaller muscle mass in the arms and shoulders than in the legs.

 

Part 4 of your lab assignment is a discussion question:

Would you expect the same drop in VO2 peak in upper body ergometry vs. lower body ergometry in a highly trained swimmer that you may expect in an untrained subject?  Why or why not?

 
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Review of Lab 3

You have come to the end of the online content of Lab 3.  Your  assignment has been presented in 4 parts, one part at the end of each section of the lab (pages 13,16,27 and 28).  You are to complete each of the questions and calculations and submit this assignment as an attachment to email.  The subject line of the email should be "your name - Lab 3" 


If you are uncertain about any concept presented in this lab, or if you want clarification or expansion of any point in the lab, I urge you to start a threaded conference discussion on WebBoard. Other students may have the same concerns, will probably benefit from the discussion, and may have the information you seek. And, of course, feel free to contact me (Dr. Eldridge) for assistance.

Be sure to check the Announcements Page to see whether there is a specific WebBoard or other assignment associated with this lab.