calculating bone density lab

8/11/2019 Calculating Bone Density Lab

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2001 UTHSCSA "Positively Aging" a trade mark of the University of Texas Health Science Center at San Antonio

LESSON FOUR: BONE DENSITY

FOCUS:There is a relationship among the structure of bones, bone mineral density, and the

strength of bones. This Positively Aginglesson will help students understand these

relationships and recognize how the strength and density of bone can reduce fractures.

OBJECTIVES: Students will: Calculate densitymass (in grams) per unit volume (in milliliters). Examine bone specimens for density and micro-structures Calculate fracture rates. Graph and interpret line graphs

ACTIVITY 4A: APPLYING THE DENSITY FORMULAThis activity is designed to be used in the math classroom. It defines variable, for-

mula, and density, and gives students the opportunity to practice calculating density byapplying the density formula. Teachers are encouraged to incorporate experiments(perhaps in science) that allow students to explore the conceptof density prior to apply-ing the definition and formula. Students will be required to calculate density duringActivity 4B. Refer to the student handout Applying the Density Formula and theaccompanying teacher answer sheet.

ACTIVITY 4B: DETERM INATION OF BONE DENSITY

W ITH BONE SPECIM ENS

A not e t o the t eacher: The objective of this activity is to allow students the opportunityto calculate the density of sectioned bone specimens. (These long bones are obtained andcut into cross sections in advance of the lab. Make sure you read through the procedures for

p reparing these specimens.)Students will investigate how the density varies at the endsof long bone and the mid-section of the shaft. Working with one bone specimen, eachlab group should conclude that there is a pattern with the bone density calculations.The density at the ends of the long bone specimen where there is spongy bone should

be less than the density anywhere along the shaft where the compact bone is present.After comparing class data, the students should conclude that there is a similar pattern

in bone density calculation among all the same types of bone specimens.


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Teacher Directions forDetermination of Bone Density with

Bone Specimens Lab

1. Students should be divided into groups of 4. Assign a number to each group.2. Each student should receive the student handouts which include:

a) the lab directions,b) a table for the groups data collection,c) a table for the classs data collection,d) a graph for the class data and group data, ande) analysis questions.

See the student handouts and answer key.3. Have students wear dissecting gloves while handling the specimens. Each group

will be given their own bone specimen that has been cut into 10 transverse sections.4. Students will determine the mass, volume (displacement method), and density

(mass/volume) of their specimen cuts. Then, each student will record the

groups data.5. The class data collection sheet will require the students to calculate the averagedensity, minimum and maximum density, range, and median density. Review howto determine these calculations with the students (refer to Unit 11, Activity 4 forexamples). Have one member from each group record their groups results on thefront board or on the teacher transparency provided for class results. Have eachstudent record the class data on their classcollection sheet on bone density.

6. Students will answer the analysis questions.7. Next, the students will complete the graphing activity. Students will graph the

average density values for the 10 specimen cuts for all the classs bones. Then, theywill graph their groups bone density values for all 10 specimen cuts from their bone.A teacher transparency of the graph is available as part of the post-lab discussion ofthe classs results. See the teacher transparency on graphing bone density. One labgroup could volunteer to graph their results on the transparency to compare withthe class density averages.

Procedure for Preparation of Specimens forDetermination of Bone Density with Bone Specimens Lab

Preparation of the materials for this lab must occur in advance to allow sufficienttime to secure the bone specimens. The source of the long bone specimens may be

obtained by contacting a local butcher or meat processing plant. A long bone from adeer, cow, or lamb would be appropriate. Obtain one long bone for each lab group offour students. Each group should work with the same type of bone.

With a bandsaw, cut the long bone into 10 transverse cuts, or ask the butcher orwoodshop teacher to assist. (The specimen slices should be cut to fit inside the size of gradu-ated cylinder you have available to measure their volume by the displacement method, or the

slices can be cut to fit into a larger beaker, then measured using the positive displacementmethod. )Make sure you number the sections, which might be easier to do if the speci-mens are allow to dry and the soft marrow removed. (The slices could also be boiled to


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clean them and to remove the marrow.) The numbering can be done with a permanentink marker, such as a Sharpie TM, then coated with clear nail polish. Number the bonesections in sequence as they were cut from the long bone.See the figure below.

Briefly discuss the concept of density as mass per unit volume of an object. Theteacher should demonstrate how to determine mass and volume of an object. Studentswill need to be familiar with determining the mass of an object using a triple beam

balance and the volume of an object by the displacement method. Review the units ofmeasurement for mass is grams and for volume is 1 cubic centimeter or 1 milliliter.Refer back to activity 4A on how to use the density formula.

ACTIVITY 4C: M AGNIFIED EXAM INATION OF BONE

SECTIONSThe objective for this lab is to allow students to observe and compare the micro-

scopic structure of compact and spongy bone. The bone specimens from activity 4Bmay be used for this activity. Students will use a hand lens or dissecting microscope toobserve and draw a bone specimen cut from the end of the long bone and from the midsection. They will answer questions to compare the location of types of bone and theirdensities calculated from activity 4B. The spongy (cancellous or trabecular) bone at the

ends of the long bone specimens should have the least density, while the specimensfrom the mid-section of the compact (or solid) bone located along the shaft should havea greater density.

ACTIVITY 4D: FIGURING FRACTURE RATES

A not e t o t he t eacher: To help doctors or researchers determine critical ages in whichfractures occur, many studies have been conducted on men and women. Doctors areanxious to figure out when the risk of fracture is highest. In order to do this, theresearchers have to take information and turn it into something that has meaning. Thestudents are going to have a chance to figure fracture rates from the data collected in astudy conducted in Canada. The authors of this study gathered data on the incidenceof hip fractures in Saskatchewan Canada, residents aged 65 years or older for the 10years between 19761985 from computerized hospital discharge records and comparedit with rates for several other populations in Northern Europe and the United States.This study was restricted to people 65 years or older because this is the populationgroup for which hipfracture has the greatest public health impact. The data used in thisactivity is taken from: Ray, W.A., M. R. Griffen, R. West, L. Strand, and L. J. Melton III.Incidence of Hip Fracture in Saskatchewan, Canada 1976-1985,AmericanJournal of Epidemiology 1990; 131: 5029.

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In this lesson, explain fracturesto students. Fractures are breaks or cracks in a bone.Point out that in older adults these breaks usually occur in the hip, wrist, or vertebraeareas. In older persons, fractured bones are often due to decreased bone mineral den-sity. That is, the lower the bone density, the greater the risk of breaking a bone (forexample, during a fall).

The Fracture rate is a ratio of the number of fractures in a group of people over a

given period of time. These ratios can be used to calculate the probability that a frac-ture will occur. This is important for doctors to know so that they can track the ages atwhich fracture is most probable.

Hand out the worksheet, Figuring Fracture Rates. The students should followalong as you explain the given information. The doctors in this study only looked atadults that had fractures occurring in the hip area. They kept up with this informationfor ten years. So, in the column labeled, # Fractures, the number represents how manyfractures occurred in that age group over a ten year period. Ask student how manyfractures occurred in women between the ages of 6569. The should respond with 347.

The next column, Person Year s, is the amount of time of exposure to the potential

event experienced by the people in the study. Person years is calculated by taking thetotal number of people in the study multiplied by the number of years they were in thestudy. So if 10 people stayed in the study for 10 years, then it would equal 100 personyears; or if 50 people were studied for 2 years, it would also equal 100 person years.How many person years are in women between the ages of 8589? Answer: 44,141.

Now to calculate the rate of fractures for every 1,000 person years, the studentshould divide the number of fractures by the total person years (e.g., 347195,647 =0.0018), and then multiply by 1,000 (0.0018 x 1,000=1.8). Work this one out on the

board with the students. Instruct the students to complete the worksheet for bothmen and women.

ACTIVITY 4E: GRAPHING FRACTURE RATESMake copies of the supplied graph for the students to use during this activity. The

students will take the answers from the previous worksheet and graph the information.They will make a double line graph (one line for men, one line for women) of the frac-ture rate per 1,000 person years, and then compare the information. After graphing,have the students answer the questions. Discuss the questions as a group. The studentsshould recognize that with age, fracture rate increases. They should also recognize thatin females the fracture rate is much greater. This is due to the fact that females tend tohave smaller bones to begin with, and they experience rapid bone loss upon the onset of

menopause. You might want to point out that the number of fractures in both malesand females aged 95+ is lower because there are fewer people in this age group.


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ACTIVITY 4A: APPLYING THE DENSITY FORMULAA variableis a letter that stands for a number. Formulasare equations that use

variables. One concept that is defined with a formula is density. Densityis a ratio ofmass to volume. The formula used to calculate density is D = m/v. This formula con-tains three variables: D stands for density, m stands for mass, and v standsfor volume.

Example: Suppose that a box has a mass of 30 grams and a volume of 6 cubic centi-meters. Find the density.

m = 30 g step 1) D = m/vv = 6 cm3 step 2) D = 30 g/6 cm3

step 3) D = 5 g/ cm3

A. Use the given information to calculate the density.

1. m = 500 g 2. m = 1,250 g 3. m = 306 gv = 20 cm3 v = 500 cm3 v = 45 cm3

4. m = 9.8 g 5. m = 549 g 6. m = 120 gv = 2 cm3 v = 36 cm3 v = 480 cm3

B. Volume can also be measured in milliliters (ml). Milliliters are used if you arefinding the volume of a liquid or using the displacement method to find the volumeof a solid (1 ml = 1 cm3). Use the information to calculate the density.

7. m = 9.8 g 8. m = 10.4 g 9. m = 15 gv = 7 ml v = 8 ml v = 6 ml

10. m = 18 g 11. m = 45 g 12. m = 240 gv = 12 ml v = 90 ml v = 80 ml

C. Now try these problems:

13. D = 1.5 g/ cm3 14. D = 3 g/ cm3

v = 16 cm m = 48 g

Find the mass. Find the volume.

15. Box 1 and Box 2 have the same mass. If the volume of Box 1 is greater than thevolume of Box 2, what do you know about their densities?


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ACTIVITY 4A: APPLYING THE DENSITY FORMULA

ANSWER KEY

A.1. 25 g/ cm3 2. 2.5 g/ cm3 3. 6.8 g/ cm3

4. 4.9 g/ cm3 5. 15.25 g/ cm3 6. 0.25 g/ cm3

B.7. 1.4 g/ml 8. 1.3 g/ml 9. 2.5 g/ml

10. 1.5 g/ml 11. 0.5 g/ml 12. 3 g/ml

C.13. mass = 24 g 14. volume = 16 cm3

15. The density of box 2 is greater than the density of Box 1.


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Problem: How does the density at the ends of a long bone compare to the density of themid-section of the shaft?

Hypothesis:

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

M aterial s: (for a group of 2 to 4 students)

graduated cylinder with an interior diameter that will accommodate the bone sections 250 ml beaker

bone sections cut from a long bone (such as cattle, sheep, or deer) triple beam balance hand lens or dissecting scope dissecting gloves 2 different color markers

Procedurefor Bone Density Lab:1. Read the problem to be investigated. Write a hypothesis.2. Weigh each dry bone section to determine its massin grams.3. Record the mass in the group data collection table.4. Determine the volumeof each bone specimen by the displacement method.

a. Measure 50 ml of water in the graduated cylinder. (This amount may need to bechanged to accommodate the size of the bone section.)

b. Place the bone section in the graduated cylinder.c. Record the amount of water displaced from the specimen (original level of water

minus the level of water with the bone section = volume of water displaced =volume of the bone section).

5. Calculate the densityof the bone specimen. Density = mass/volume = grams/ml.6. Record the density of each specimen cut on your group data collection sheet.7. Have one member of the lab group record the groups results on the teacher

transparency for the class data.8. Record the class results on your class data collection sheet.9. Using a color of your choice, make a line graph of the class average densities for

each groups bone specimen on the graph sheet. Make a color key and label theline Class Bone Density Averages.

10. Make another line graph of your groups density values for each of the 10 specimencuts on the same graph sheet you just used. Use a different color from the one instep 9 and labelthe line Group Bone Density.

11. Answer the analysis questions.


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GROUP DATA COLLECTION SHEET

Name________________________________ Student Group #__________ Date _________

BoneSketch

BoneSection #

Mass(grams)

Volume(milliliters)

Density(g/ml)

1

2

3

4

5

6

7

8

9

10


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GROUP DATA COLLECTION SHEET

BoneSketch

BoneSection #

Mass(grams)

Volume(milliliters)

Density(g/ml)

1

2

3

4

5

6

7

8

9

10


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Bone

Ske

tch

1 2 3 4 5 6 7 8 9 10Bone

Sect

ion

#

Group

1

Group

2

Group

3

Group4

Group

5

Group

6

Group

7

Average

Densi

ty

Mini-

mum

Maxi-

mum

Range

Me

dian



CLASS DATA COLLECTION SHEET



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CLASS DATA COLLECTION SHEET

Bone

Ske

tch

1 2 3 4 5 6 7 8 9 10Bone

Secti

on

#

Group

1

Group

2

Group

3

Group4

Group

5

Group

6

Group

7

Average

Densi

ty

Mini-

mum

Maxi-

mum

Range

Me

dian


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ACTIVITY 4B: DETERM INATION OF BONE DENSITY WITH

BONE SPECIM ENSGRAPHING BONE DENSITY


BONEDE

NSITY(gm

/ml)

1 2 3 4 5 6 7 8 9 10Bone Section Number

2001 UTHSCSA "Positively Aging" a trade mark of the University of Texas Health Science Center at San Antonio 12-12


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ACTIVITY 4B: DETERM INATION OF BONE DENSITY W ITH

BONE SPECIM ENSGRAPHING BONE DENSITY

BONEDE

NSITY(gm

/ml)

1 2 3 4 5 6 7 8 9 10Bone Section Number


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BONE SPECIM ENS

ANALYSIS QUESTIONS

1. Examine your groups data on bone density. What is the location of the specimencut with the: greatest density? __________________

smallest density? __________________

2. Examine the class data on bone density. How does the average density at theends of the long bone compare to the average density at the mid-section shaft of thelong bone?___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

3. Observe your graph of the class average bone densities and your groups bonedensity values. Also, look at the section of the bone that has the highest and lowest

bone densities. Describe any pattern you observe between the bone densities andthe location of the bone specimen cut.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

4. Examine why there may be differences in bone density values among the differentlab groups.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________


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BONE SPECIM ENS

ANALYSIS QUESTIONS Answer Key

1. The greatest bone density should be from a bone specimen cut toward the middle ofthe shaft of the long bone. The smallest bone density should be from a bonespecimen cut located at the end of the long bone.

2. The average bone density of all the bones should be greatest towards the middle ofthe shaft of the long bone. The smallest average bone density of all the bones should

be at the ends of the long bone.

3. The graph of the class average bone densities should follow a similar pattern withthe groups bone density values. The greatest bone density values should be towardthe middle of the shaft of the long bone, and the smallest bone density values should

be at the ends of the long bone.

4. Differences in bone density values for each bone specimen cut among the bones usedin the different lab groups could be due to the age of the animal, disease, nutrition,and accuracy of measurement.

SKETCH OF AN END SKETCH OF A MID-SECTION OF A LONG BONE OF A LONG BONE


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ACTIVITY 4C: M AGNIFIED EXAM INATION OF

BONE SECTIONS


Directions:

1. Use a hand lens or dissecting scope to examine a section of bone from an end of thebone and another section of bone from the middle of the bone.

2. Make a sketch of each bone specimen in the boxes below.

SKETCH OF AN END SKETCH OF A MID-SECTION OF A LONG BONE OF A LONG BONE

Anal ysis Quest i ons for M agnif i ed Examinat i on of Bone Sect i ons

1. Identify the type of bone found at the end of the long bone specimen (refer to lesson2 on bone anatomy). __________________________________

2. Identify the type of bone found at the mid-section of the long bone specimen (referto lesson 2 on bone anatomy). __________________________________

3. What can you conclude about the structure of the bone sections from the long bone,

their bone densities, and how they compare?

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________


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ACTIVITY 4C: M AGNIFIED EXAM INATION OF

BONE SECTIONS

Answer Key

Sketches:

The sketch of the end of a long bone should show a loose arrangement of bone tissue(porous), and the sketch of a mid-section of long bone should show a very compactarrangement of bone tissue.

Anal ysis Quest i ons:

1. Spongy or cancellous bone2. Compact or solid bone3. Spongy bone found at the ends of a long bone has a smaller bone density than

compact bone found at the shaft of the long bone.


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ACTIVITY 4D: FIGURING FRACTURE RATE

Use the chart below to help figure the hip fracture rate in both men and women.To figure the rate, you must divide the number of fractures by the person years. Theanswer is the rate of fractures for every 1,000 person years. To express this number asthe rate of fracture for every 1,000 person years, multiply by 1,000 and round to the

nearest tenth.

FRACTURE RATES FOR WOMEN

Number of Age Group Fractures Person Years Rate Per 1,000

6569 347 195,647 _________

7074 546 155,637 _________

7579 741 112,404 _________

8084 944 74,987 _________

8589 1,056 44,141 _________

9094 631 18,924 _________

95+ 221 5,418 _________

FRACTURE RATES FOR MEN


6569 170 184,427 _________

7074 237 143,561 _________

7579 313 97,994 _________

8084 361 58,412 _________

8589 382 30,863 _________

9094 239 12,639 _________

95+ 79 3,187 _________


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ACTIVITY 4D: FIGURING FRACTURE RATE

Answer Key

FRACTURE RATES FOR WOMEN


6569 347 195,647 _________

7074 546 155,637 _________

7579 741 112,404 _________

8084 944 74,987 _________

8589 1,056 44,141 _________

9094 631 18,924 _________

95+ 221 5,418 _________

FRACTURE RATES FOR MEN

Number of

Age Group Fractures Person Years Rate Per 1,000

6569 170 184,427 _________

7074 237 143,561 _________

7579 313 97,994 _________

8084 361 58,412 _________

8589 382 30,863 _________

9094 239 12,639 _________

95+ 79 3,187 _________

1.8

3.5

6.6

12.6

23.9

33.3

40.8

0.9

1.7

3.2

6.2

12.4

18.9

24.8


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USE FOR MENUSE FOR WOMEN

50

45

40

35

30

25

20

15

10

5

0

HIPFRACTURERATEPER1

,000

PERSONYEARS

6569 7074 7579 8084 8589 9094 95+

AGE GROUPS (years)

ACTIVITY 4E: GRAPHING FRACTURE RATES


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ACTIVITY 4E: GRAPHING FRACTURE RATESAnswer Key

6569 7074 7579 8084 8589 9094 95+

AGE GROUPS (years)

USE FOR MENUSE FOR WOMEN

50

45

40

35

30

25

20

15

10

5

0

HIPFRACTURERATEPER1

,000

PERSONYEARS


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ACTIVITY 4E: FRACTURE RATE GRAPH QUESTIONS

1. According to the graph, what trend is seen as a person ages?

2. Is there a difference between the fracture rates in men and women? Why do

you think that?

3. Why do you think fracture rates increase with age?

4. The hip is one of the most common body sites for fractures. Why do you think it issuch a common break site?


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ACTIVITY 4E: FRACTURE RATE GRAPH QUESTIONS

Answer Key

1. According to the graph, what trend is seen as a person ages?

As a person ages the chances of bone fractures occurring increases.

2. Is there a difference between the fracture rates in men and women? Why doyou think that?

The fracture rate in men is lower than in women. Men have greater bone

density to begin with and have less bone loss over time than women.

3. Why do you think fracture rate increases with age?

As a person ages their bones become less dense which makes it easier for a

bone to break.

4. The hip is one of the most common body sites for fractures. Why do you think it is

such a common break site?

It is a weight-bearing bone. It is also the end of a bone which is less dense

than the middle of the bone. Breaks usually occur at the end of a bone.

(Note: other osteoporotic sites with cancellous bone that fracture include

the vertebral bodies and the radius near the wrist).

calculating bone density lab

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