Tornetta Rockwood Adults 9781975137298 V2

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SECTION ONE • General Principles

vertebral body, resulting in an increased risk of vertebral com- pression fractures in individuals with osteoporosis. Density plays a vital role in determining the structural prop- erties of bone. The material properties of a single trabecular bone spicule and a similar sized sample of cortical bone are comparable, with stiffness and strength measurements differing by less than 10% to 15%. Measuring strength and stiffness at the structural level shows trabecular bone is far weaker than cortical bone. The structural stiffness and strength of trabecular bone are defined by its porosity that, depending on the individ- ual and anatomic location, ranges from 30% to 90%. Clinically, the density of trabecular bone is measured by radiographic den- sitometry and can vary by one order of magnitude, from about 0.1 to 1.0 g/cc. The corresponding stiffness and strength of tra- becular bone vary by up to three orders of magnitude, meaning that even small decreases in density can significantly weaken the structural properties of trabecular bone. LOAD TRANSFER THROUGH JOINTS AND FRACTURES Joints enable motion between bone segments. Joint motion is controlled by the forces and moments acting across joints. Forces acting on a joint are typically represented by vectors, depicting the magnitude and line of action of a force. If a force vector of magnitude F is acting at a distance d from a joint, it will also create a rotational moment M around the joint. This moment has a magnitude of M = F × d , whereby M linearly increases with the distance d , or “lever arm,” of the force vector from the joint. Unless it is counteracted by a moment of equal magnitude in the opposite direction, this moment will induce rotation at the joint. A seesaw illustrates this important lever arm concept (Fig. 1-5A). If a person sits at a greater distance from the fulcrum around which the seesaw pivots, the person has a greater “leverage” or mechanical advantage, and can exert a greater force than the person sitting closer to the fulcrum. A seesaw or a joint is in equilibrium if the clockwise and counter- clockwise moments are of equal magnitude. Joint forces and resulting moments are induced by external loads such as the weight of an object held in a hand, and by internal loads such as the muscle forces required to hold the object. External forces can be measured readily with scales and load sensors that determine the force acting on the body. Inter- nal load assessment is far more complicated because muscles cannot be instrumented with load sensors and because multiple muscles with various degrees of activation act across the same joint. However, when a joint is at rest or in a “static equilib- rium,” joint forces can be calculated based on two equilibrium requirements: the sum of all forces and the sum of all moments acting on a static joint must be zero. For this purpose, known external forces are plotted on a “free body diagram,” along with the line of action of muscle forces that must generate the inter- nal loads to achieve static equilibrium. For example, a free body diagram can be drawn to calculate the forces on the elbow joint while holding a water bottle (Fig. 1-5B). A 1- liter water bottle exerts a downward force of approximately 10 N. Since this force acts at a distance of 0.3 m from the elbow, it also induces an extension moment M = 10 N × 0.3 m = 3 Nm around the elbow. Assuming that the biceps is the sole elbow

A

B

C

flexor, the biceps muscle must create a flexion moment of equal magnitude for static equilibrium to exist. Since the biceps force acts at a distance of only 0.03 m to the elbow joint, it must gen- erate a force of F = 3 Nm/0.03 m = 100 N to counteract the extension moment. It is important to note that the biceps has a 10 times shorter lever arm than the water bottle, and there- fore requires 10 times more force to counteract and equilibrate the moments around the elbow joint. For the second require- ment of the free body diagram, the sum of all forces must also be Figure 1-5.  A: A seesaw illustrates how a longer lever arm requires less force to achieve the same moment around fulcrum A than a shorter lever arm. B: A free body diagram of the elbow enables calculation of joint loads. Since the biceps has a 10 times shorter lever arm than the water bottle, the biceps requires 10 times more force to counteract and equilibrate the moment around the elbow joint that is generated by the water bottle. C: A fixation construct must equilibrate the bend- ing moments of the diaphysis around the fracture site. A short fixation construct will exhibit higher stress than a longer construct, owing to its shorter lever arm available to counterbalance bending loads.

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