Summary of Key Points
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In distraction, when applied away from the instantaneous axis of rotation (IAR), the resultant force develops a bending moment. When applied close or in line to IAR, it is very effective at resisting axial loading. This technique is usually not used alone.
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In three-point bending fixation, the resulting fulcrum directs a force vector opposite the direction of the terminal force vectors. It is usually used along with distraction. The bending moment generated is proportional to the length of the construct.
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In tension band (compression) fixation, the magnitude of the bending moment is the result of the compression force applied by the tension band and by the perpendicular distance from the IAR to the applied force.
Surgeons and engineers who use and design spinal implants must understand the forces acting on the implant and the spine for successful application. These forces are complex and constantly change as the patient moves, the spine heals, and the spine-implant interface degrades.
Instrumentation techniques exert forces to the spine through six basic mechanisms: distraction, three-point bending, tension band fixation, fixed moment arm cantilever beam fixation, non–fixed moment arm cantilever beam fixation, and applied moment arm cantilever beam fixation. All of these mechanisms can be used individually or in combination. This chapter discusses in detail how various types of distraction, compression, and three-point bending implants carry these forces and redistribute them to the remainder of the spine and surrounding tissues. Strategies are presented that can help prevent overloading any portion of the spine-implant combination (construct) and subsequent failure. The information presented in this chapter is an overview; more in-depth information may be gleaned from numerous sources. Implant-specific information is also available.
Distraction Fixation
The use of distraction can be very effective in reestablishing spinal height. It can be applied from either a ventral interbody or a dorsal approach. However, it is uncommon to use distraction alone because it is difficult to apply forces directly in line of the instantaneous axis of rotation (IAR) or symmetrically around it. When distraction is applied away from the IAR, the resultant force develops a bending moment, as shown in Figure 41-1 .

If we know the magnitude, the point and line of application of the distraction force and the location of the IAR, we may predict the response of the spine segment. In these cases, the bending moment results in compression of the spine on the opposite side of the IAR from the site of distraction force application ( Fig. 41-2 ).

The ability to resist bending (originated from the distraction) is called moment of inertia ; this is usually derived from intrinsic spinal elements (e.g., ligaments). The moment of inertia can be increased by tensile structures (ligamentous or implant) that are farther from the IAR than the distraction forces. The bending moment can be eliminated by balancing the distraction and tensile forces as shown in the following equation:
F d × d d + F t × d t = 0
The development of bending moments is particularly problematic when the isolated distraction forces are applied dorsal to the IAR. This force has the propensity to exaggerate pathologically or cause a kyphotic deformity. Simple dorsal distraction is uncommonly applied, although it can be combined with three-point bending fixation to impart desirable results.
Ventral distraction constructs (interbody region) generally apply forces that are closer to or in line to the IAR. When applied in line to the IAR, they become very effective in resisting the bending moments caused by axial loads applied through the center of gravity. In addition, this application of forces results in less compression of the contralateral side of the IAR. When the interbody distraction force is applied ventral to the IAR, it generates a bending moment, which causes extension in the spine. These implants can be placed either in an active mode to decompress the fracture or in a neutral mode to resist recompression when the patient assumes an upright posture.
Three-Point Bending Fixation
When a pencil is pushed with the thumbs together in the center and the fingers at the ends pushing in opposite direction, we are exerting a three-point bending force. The resulting fulcrum directs a force vector opposite the direction of the terminal force vectors. This central force vector has twice the magnitude of the sum of the terminal force vectors ( Fig. 41-3 ). In the clinical scenario, three-point bending spinal instrumentation applies similar force vectors. They are usually, but not always, applied with an accompanying distraction force by using instrumentation such as Harrington distraction rods or universal spinal instrumentation.

The bending moment generated by a three-point bending fixation construct is proportional to the length of the construct. Three-point bending implants usually involve the application of dorsal instrumentation over multiple spinal segments (five or more spinal segments). The forces at the rostral and caudal implant-bone interfaces are usually dorsally directed. The central force is usually in the ventral direction. This central force is equal to the sum of the two dorsally directed forces and is normally located over the dorsal surface of the vertebra that requires decompression (see Fig. 41-3 ). If the dorsal surface of this central vertebra is damaged so that it would not resist the application of the force, the location of ventral force application can be moved to the vertebrae above and below the damaged vertebra. The result is four-point bending fixation . The effects are similar to three-point bending fixation, but larger forces or longer moment arms (more spinal segments) are required to obtain the same bending moment and decompression. Using the previous example with a pencil, this concept can be visualized by moving the thumbs apart while keeping the fingers in the same location when bending the pencil.
The maximum bending moment (M 3pb ) in three-point bending fixation occurs at the location of the central force and is described by the following equation:
M 3 pb = F r × l r = F c × l c
The forces and lengths are as defined in Figure 41-4A , and the system is assumed to be at rest. The requirement that the sum of the three forces be zero can be used to derive the moment in terms of the central force, as follows:
M 3 pb = F cent l r l c l r + l c l t = F cent l r l c

Examination of this equation shows that the largest moment is obtained when the lengths of the two moment arms are equal and hence the terminal forces are the same, as follows:
F r = F c = 0.5 F cent L r = l c = 0.5 l t M 3 pb max = 0.25 F cent l t

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