Bone Density & Osteoporosis
Calculating Density
Case Study – Background & Introduction
Your bones are constantly rebuilding themselves. As cells die, your body produces new cells to replace them. If your body cannot keep up with producing new cells, you may develop more open space within your bones. The condition associated with low bone density is called osteoporosis.
There are a few reasons that people develop osteoporosis. In order to build new bone cells your body needs to absorb calcium. Taking calcium supplements or increasing your intake of calcium rich foods like dairy, certain vegetables and seafood can help you avoid bone loss. In order to absorb the
calcium you need Vitamin D, which is why milk and other products are fortified by adding in vitamins.
Activity is also essential for building bones. If you reduce the impact felt by your bone cells there will be increased bone resorption (which means that more bone cells will begin to die) and there is reduced formation of new cells. Astronauts actually have 1.5% bone loss each month they are in space because their bone cells don’t experience much impact and don’t have to fight gravity. This means that if they stay for 6 months they can lose 10 percent of their bones! It can take up to 4 years for them to truly recover. This is why you might see astronauts doing a lot of exercising in space – it’s not just to stay fit, but it is also to stimulate their bone cells to form.
Although not as severe as an astronaut’s experience, your own inactivity can reduce your bone strength. As people age they tend to decrease their calcium intake, and also decrease their activity. In women, Estrogen helps to protect bones, so after menopause that protection ends and can greatly increase bone loss.
These combined with genetic predispositions and
changes in the amount of calcium you need, can result in a severe decrease in bone density. This means that a small fall will result in severe fractures and long term recuperation.
From the age of 20 to 80, women lose 1/3rd of their bone density, and men lose 1/4th, which is why women tend to have more issues with osteoporosis. Caucasian women in particular have a genetic predisposition for bone loss so they are at the most risk.
Name(s): Period: Date:
courses.washington.edu/bonephys/opbmd.html https://www.nia.nih.gov/health/publication/menopa use‐time‐change/postmenopausal‐health‐concerns
NASA.gov
Bone Density & Osteoporosis
Density Calculations
Objectives
HSN‐Q.1 – Use units as a way to understand problems and to guide the solution of multi‐step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays HSA‐CED.4 – Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
HSG‐GMD.3 – Use volume formulas for cylinders, pyramids, cones and spheres to solve problems HSG‐MG.1 – Use geometric shapes, their measures and their properties to describe objects HSG‐MG.2 – Apply concepts of density based on area and volume in modeling situations
Scenario
In order to find the bone density on a living person, a radiologist takes an x‐ray of the bones. The computer uses complex mathematical calculations to extrapolate the density of the bone based on the exposure levels of the x‐ray. In this mathematical exercise you will use the density equation and apply it to simulated samples that you would have taken if you were to sample the bone directly.
Calculating Density
Density is a measurement that relates the volume of an item with its mass. Just because
something weights a lot doesn’t make it dense. Compare in your mind a pound of feathers and a pound of rocks. Which one weighs more? Trick question – they weigh the same. The difference is the volume they take up. This is because the rocks are more dense, so they take up less space based on their mass.
Use the following equation to answer the following problems:
Directions
Find the density of each bone sample, and give a diagnosis of Normal, Osteopenia or Osteoporosis
Patient #1: A 1cm3 sample was taken and it weighed 900mg
density: diagnosis:
Work:
Patient #2: A 1.5cm3 sample was taken and it weighed 1000mg
density: diagnosis:
Work:
Patient #3: A 0.75cm3 sample was taken and it weighed 600mg.
density: diagnosis:
Work:
Patient #4: A 0.5cm3 sample was taken and it weighed 350mg.
Name(s): Period: Date:
>833 mg/cm3
Normal Bone Density Osteopenia 833‐648 mg/cm3
<648 mg/cm3 Osteoporosis
Using geometry to find density
If you look at a bone, the middle section, known as the diaphysis, is in a cylindrical shape. Use the equation to find the volume of a cylinder in order to calculate volume, or find the volume of the rectangular prism, then divide mass over volume to find density. Report density in mg/cm3. 1g=1000mg
Patient #5: What is the density if the length of the diaphysis sample is 8.0cm, the diameter is 3.0cm and the mass of the sample is 41g (41,000mg)
density: diagnosis:
Work:
Patient #6: What is the density if a 2.5cm cube of bone weighs 8.75g?
density: diagnosis:
Work:
Patient #7: What is the density if the length of the diaphysis sample is 12cm, the diameter is 5.8cm and the mass of the sample is 20g
density: diagnosis:
Work:
Patient #8: What is the density of a 7.4g sample if the length of a rectangular prism of bone is 4.5cm, the height is 1.2cm and the depth is 2.5cm.
density: diagnosis:
Work:
Patient #9: What is the density if the length of the diaphysis sample is 3.0cm, the diameter is 2.2cm and the mass of the sample is 10.8g.
density: diagnosis:
Work:
Patient #10: What is the density of a 43.5g sample if the length of a rectangular prism of bone is 6.8 cm, the height is 3.2cm and the depth is 2.9 cm.
density: diagnosis:
Work:
Patient #11: What is the density if the length of the diaphysis sample is 6.0cm, the diameter is 4.2 cm and the mass of the sample is 92g.
density: diagnosis:
Work:
https://en.wikipedia.org/wiki/
Diaphysis
Rearranging the equation
Patient #12: This patient has a bone density of 820mg/cm3. What is the volume of a 25g sample?
Volume (in cm3) diagnosis:
Work:
Patient #13: The patient has a bone density of 1200mg/cm3. What is the mass of a 39.5cm3 sample?
Mass (in grams) diagnosis:
Work:
Patient #14: This patient has a bone density of 635mg/cm3. What is the volume of a 43g sample?
Volume (in cm3) diagnosis:
Work:
Patient #15: The patient has a bone density of 725mg/cm3. What is the mass of a diaphysis sample with a diameter of 3.0cm and a length of 9.8cm?
Volume (in cm3)
Work:
Mass (in grams) diagnosis:
Work:
References
https://courses.washington.edu/bonephys/opBMAD.html
http://www.mayoclinic.org/diseases‐conditions/osteoporosis/basics/definition/con‐20019924 http://nof.org/articles/886
http://www.nasa.gov/mission_pages/station/research/benefits/bone_loss_prt.htm http://www.everydayhealth.com/osteoporosis/osteoporosis‐and‐gender.aspx
https://www.nia.nih.gov/health/publication/menopause‐time‐change/postmenopausal‐health‐
concerns
Key
Patient Density in mg/cm3 Diagnosis
1 900 Normal
2 667 Osteopenia
3 800 Osteopenia
4 1200 Normal
5 725 Osteopenia
6 1400 Normal
7 630 Osteoporosis
8 550 Osteoporisis
9 950 Normal
10 690 Osteopenia
11 1100 Normal
12 Volume: 30.5cm3 Osteopenia
13 Mass: 47.4g Normal
14 Volume: 67.7cm3 Osteoporosis 15 Volume: 69.27cm3
Mass:50.2g Osteopenia
