Biomechanics

The primary responsibility of the skeleton is to withstand loadbearing. Bone is strong, it is stiff, it is tough. Bone can withstand extremely high loads, and will remain strong even following several million cycles of load. We, as scientists, can learn a tremendous amount by studying how nature has, over the past several hundred million years, figured out how to how to design this wonderful material. Understanding a few basic elements of mechanics allows the scientist, physician, engineer, and even architect, to appreciate how nature has achieved a solution to a demanding task, such as holding up a one ton animal who runs at very high speeds.
 
If you, as a scientist, engineer, architect or physician, were to design the ultimate material, bone could teach you a lot about the mechanics and design of a structure. Below are some mechanical criteria essential to any structure. The terms as used by scientists have very specific meanings:

STRAIN
When a force is applied to any material, such as bone, it deforms. The amount of deformation in the material relative to its original length, is the strain. When a material is pushed together, the material shortens (compressive strain). When pulled, it gets longer (tensile strain). Shear strain arises when layers of a material slide against another, as might occur with torsion or bending. The strain can be expressed as a percentage (100 x change in length/original length). When your muscle contracts, the tendon can strain as much as 5% in tension during intense activities. Compressive strains in bone during peak activities only rise to about 0.3% strain, and bone begins to fail at 0.7% strain (7000 microstrain).
 
STRESS
To have stretched or compressed the bone, a force had to be applied to it. The force per unit area is the stress, and is reported in Newtons per square meter, or Pascals. A Pascal is essentially the stress caused by the weight of one apple (0.1Kg) acting on a square meter tabletop. One million Pascals (1 MPa) is 10kg per cm2 of bone. Imagine the stress on your knee as you are standing. The force applied to your knee is your weight, acting upon the top of your tibia. The stress caused in the third metacarpal of a thoroughbred racehorse during a gallop is on the order of 63,000,000 Pascals. Now imagine 63 million apples on that same kitchen table.


Stress-strain curves


Areal properties

The properties of bone described above are material properties, which can be measured from any small segment of bone. The structural properties, which define the overall pattern of the bone, are also important to the ultimate success of the skeleton. Consider a pencil, for example. Axial loading (pressing straight down on the long axis of the pencil) results in very little strain. But consider how easily the pencil is snapped when it is subject to bending. Bone must resist complex forces, and must also remain light enough to allow speed and dexterity.
The cross-sectional areas of these 3 cylinders are identical, and they have the same elastic modulus. For an axial force (i.e., pushing or pulling the ends of the bar) the stress is also identical. BUT, the ability to resist bending is strongly dependent on the distance of the material relative to the center of the cylinder. Notice how much stronger the larger cylinder is. The mid-sections of the long bones in the arms and legs are shaped like cylinder B. They gradually become wider and thinner as adults reach old age.

References

1. Currey, J. D.(1999). The design of mineralised hard tissues for their mechanical functions. J Exp Biol 202 Pt 23: 3285-94.

2. Rubin CT and Rubin J. Biomechanics of Bone. in Favus MJ, ed. Primer on the Metabolic Bone Disease and Disorders of Mineral Metabolism. Lippincott William & Wilkins, Philadelphia, 1999 p. 39-42.

3. Turner CH and Burr DB. (1993) Basic biomechanical measurements of bone: a tutorial. Bone 14:595-608.

4. Cullinane DM and Einhorn TA. Biomechanics of Bone. in Bilezikian, Raisz, Rodan eds. Principles of Bone Biology, Academic Press, San Diego, 2002 p. 17-32.


2003 by Clinton Rubin and Susan Ott
Last update: 10/21/03

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