Limb Lengthening

Bones of a living person may behave quite differently from bone taken from a corpse and dried. Living bone is self-repairing. Alterations in the distribution of stress in a bone could yield in significant growth or remodeling. In the low-gravity situation of space flight, the compressive stresses acting on the bones are much less than that on earth, and bones lose thickness and strength. On the other hand, on earth, the bones of the leg, which carry the weight of the body, thicken with age.

Orthopaedic surgeons have begun exploiting the relationship between bone stress and bone growth to correct skeletal abnormalities. In the 1940s, in an isolated hospital in Siberia, Professor Gavriil Ilizarov came up with an ingenious method to treat limb length inequality, congenital limb deficiency, and other types of bone or joint deformities. Limb correction (lengthening) is reshaping of a limb involving little invasive treatment. The procedure was described at length by Dr. Ilizarov in an article entitled "Clinical Application of the Tension-Stress Effect for Limb Lengthening" that appeared in 1990 in Clinical Orthopaedics and Related Research. Briefly, an external fixator (much like a bone scaffold) is applied on the affected bone (Fig. 6.14). The fixator is composed of a series of stainless steel cir-

Figure 6.14a-c. Schematic drawing of limb-lengthening procedure as applied to the leg of a man (a). Two steel pins are inserted at cross sections A and B on the two ends of the femur (b). While A is kept stationary with respect to the thigh, B can be moved along the axis of the bone. The bone is separated into two parts in the midregion and the distance between A and B is slightly increased. Soon new bone will form in the cracked region. The two different types of fractures used in the operation are shown in (c).

Figure 6.14a-c. Schematic drawing of limb-lengthening procedure as applied to the leg of a man (a). Two steel pins are inserted at cross sections A and B on the two ends of the femur (b). While A is kept stationary with respect to the thigh, B can be moved along the axis of the bone. The bone is separated into two parts in the midregion and the distance between A and B is slightly increased. Soon new bone will form in the cracked region. The two different types of fractures used in the operation are shown in (c).

cular rings that are attached together by threaded rods. Each ring is attached to the limb through the bone by taut steel wires and thicker titanium pins. Two wires that are perpendicular to each other cross through the bone, keeping the bone stationary relative to the external fixator.

Then, the bone is cut in half through a small incision with minimal damage to the surrounding muscle tissue. The distance between the two rings is increased slightly. in response to the sudden relaxation of stress, the surface of separation acts much like a growth plate. in the fracture gap, fibroblasts secrete and arrange new collagen fibers along the long axis of the bone. Osteoblasts use these newly formed fibers as templates to form new bone. The gap is filled by this fresh tissue in 4 to 5 days. After that period, the distance between the pins is increased at small increments (1 mm/day). This procedure is called distraction. Elongation of the freshly formed bone tissue stimulates further growth and remodeling. With time, the new bone gains the ultimate strength of the old bone. When this procedure is applied to the thigh or lower leg of a patient, he or she continues to have the use of the leg while the bone growth and remodeling occurs. However, the load that would normally be carried by the bone is transmitted through the pins to the scaffold.

The procedure described here uncovered the fact that a surgeon can create a growth plate anywhere in bone with appropriate conditions of bone fracture, fixation of the separated bone segments, and distraction. The formation of new bone only in a fracture surface (or growth plate in children and adolescents) may be a reflection of the contact inhibition of growth of biological cells. Cells grown in a culture will continue to divide until they cover the entire surface area of the plate. Cell division ceases with the establishment of multiple physical contacts with the neighboring cells. Cancer cells, on the other hand do not observe contact inhibition, and they grow to form multiple cell layers in a culture dish.

Example 6.10. Limb-Lengthening. A 17-year-old girl with 5-cm tibial shortening underwent a single-fracture limb-lengthening. Determine the physical stress in the tibia and the surrounding soft tissue when the body is in upright configuration. The girl weighed 54 kg. The initial length of her lower leg (L) was 22 cm. The average outside radius of the lower leg (Rm) was 3.5 cm. The average radius of the tibia (Rb) was 1.3 cm. Young's modulus of the soft tissue surrounding the bone (Em) was 100 N/cm2. The initially imposed gap between the adjacent surface of fracture (A) was 2 mm.

Solution: The free-body diagram of the lower leg in the standing position is shown in Fig. 6.15. The lower leg is modeled as a concentric circular cylindrical column composed of bone and the surrounding soft tissue. A compressive force that is equal to half the body weight is assumed to act on the flat top surface of the column. With this assumption, we have lumped the mass of the lower leg with the rest of the body and po-

sitioned it on top of the column. As shown in the figure, the net effect of the external fixator on the bone can be represented by a pair of equal and opposite forces acting in the vertical direction. The magnitude of this force is denoted by F. The part of the cylinder identified with the symbol I in the figure is under a uniform compressive force of W/2. In this region, at section AA', the stress distribution must obey the following relation:

where ab and am represent the axial stress in the bone and the soft tissue, respectively.

How do we determine the relative values of ab and am? The stress in the soft tissue can be computed using Hooke's law:

am = Em e = Em A/L = 100 N/cm2 (0.2/22) = 0.91 N/cm2

Substituting this value into Eqn. 6.35, we obtain

-3.14 (1.3 cm)2 ab + 3.14 [(3.5 cm)2 - (1.3 cm)2] (0.91 N/cm2)

Thus, the bone carries 50-fold-greater stress than the surrounding soft tissue. Next, we consider the stress distribution at cross section BB'. Because the bone is separated into two parts in that region, it carries no stress and the resultant force on this cross section from the stress in the soft tissue must be equal to (F - W/2):

Because am is uniform throughout the length of the cylinder, we can use this equation to determine F:

Thus, the force F is slightly greater than half the weight of the girl.

As the new bone tissue fills the gap in between the separated bone segments, the bone will begin to carry low levels of tensile stress. When the bone is distracted stepwise, this new bone will be stretched by the step of distraction.

Getting Started With Dumbbells

Getting Started With Dumbbells

The use of dumbbells gives you a much more comprehensive strengthening effect because the workout engages your stabilizer muscles, in addition to the muscle you may be pin-pointing. Without all of the belts and artificial stabilizers of a machine, you also engage your core muscles, which are your body's natural stabilizers.

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