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Biomedical Engineering DISCUSSION
In a biomaterials course we were told that a hip stem made from a very stiff metal can cause the surrounding bone to weaken over time, and that this is one reason titanium alloys are used for stems even though cobalt-chromium is stronger in some respects.
How does implant stiffness affect the load in the bone? I would like a simple calculation that shows the effect, and an idea of what else limits the choice of material.
Bone adapts to the load it carries: it is maintained where it is stressed and resorbed where it is not. A stem inside the femur shares the load with the bone around it, and the stiffer of the two carries more. If the implant takes most of the load, the adjacent bone is under-stressed, loses density over the years, and the fixation can eventually loosen. That is stress shielding.
The mismatch is large. Cortical bone has an elastic modulus of roughly 10 to 20 GPa. Titanium alloy Ti-6Al-4V is about 110 GPa, stainless steel about 190 to 200 GPa and cobalt-chromium alloys about 210 to 230 GPa.
A simple model: treat stem and bone as two bars in parallel that must strain equally. Each carries load in proportion to its axial stiffness E × A. The bone's share is E_b × A_b / (E_b × A_b + E_s × A_s). With equal cross-sectional areas and 18 GPa for bone, the bone carries 18 / (18 + 110) = 14 percent with a titanium alloy stem and 18 / (18 + 220) = 7.6 percent with cobalt-chromium.
So the bone still loses most of its load with titanium, but it keeps almost twice as much as with the stiffer alloy. Real load transfer involves bending and depends on the stem length and fixation, so this is an illustration of the trend only.
Geometry matters as much as modulus, because what counts is stiffness: E × A in compression and E × I in bending. The bending stiffness of a round stem goes with diameter to the fourth power, so a thick stem of a low-modulus alloy can be stiffer than a slim one of a high-modulus alloy. Designers reduce stiffness with tapered, slotted or hollow stems, shorter stems, and porous or lattice structures made by additive manufacturing, which bring the effective modulus closer to bone.
Lower-modulus beta titanium alloys, in the range of roughly 55 to 85 GPa, were developed for the same reason.
Stiffness is one requirement among several. The stem sees of the order of a million load cycles per year, so fatigue strength in a corrosive, body-temperature environment is critical, and surface features such as porous coatings can reduce it. Titanium alloys have excellent corrosion resistance and bone grows onto them well, but they wear poorly as a bearing surface, which is why the femoral head is usually cobalt-chromium or ceramic on a titanium stem.
Every material also has to pass biological evaluation for the type and duration of body contact, covered by the ISO 10993 series, before its mechanical merits count for anything.
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