D5 Characterization of Biological Materials

Topic

The characterization of biological materials applies solid mechanics and rheology to determine the mechanical properties of the tissues constituting the musculoskeletal system—bone, cartilage, tendon, ligament, muscle, and fascia—which serve as the structural materials underpinning movement. Unlike engineering materials, which are typically homogeneous, these biological tissues are heterogeneous and exhibit different behaviors depending on the direction of the applied load; furthermore, they are viscoelastic, meaning their mechanical behavior is strongly influenced by their loading history, hydration level, and temperature.

The mechanical properties of these tissues are determined through uniaxial tension and compression tests, which generate a curve relating applied force to resulting deformation. From this curve, one can derive the tissue's stiffness within its linear region and its fracture strength—that is, the maximum stress the tissue can withstand before failing. In soft tissue, the curve initially displays a low-stiffness phase, during which misaligned collagen fibers gradually align with the direction of the load; only after this alignment occurs does the tissue enter the linear region characterized by high stiffness.

The viscoelastic nature of these tissues, mentioned earlier, is quantified using two complementary tests: in a stress relaxation test, the tissue's deformation is held constant while the force required to maintain it is observed to decay progressively toward an equilibrium value; conversely, in a creep test, the applied load is held constant while the tissue's deformation is observed to increase over time. A model combining a purely elastic component with one that blends elasticity and viscosity captures both behaviors using just three parameters: the tissue's instantaneous stiffness, its equilibrium stiffness after relaxation, and the characteristic time required to transition between the two.

Within each of the collagen fibers that align during loading—as noted in the previous mechanical test—there are individual collagen fibrils; these can be characterized separately at the nanoscale using a microscope capable of sensing the contact force of its own probe tip. Pressing this tip against individual collagen fibrils yields stiffness values ​​between one and five gigapascals—far higher than the stiffness exhibited by the same collagen when measured as part of the whole tissue.

In the specific case of bone, structural stiffness is not measured directly via mechanical testing but is instead estimated from mineral content. Bone densitometry measures the amount of mineral present and its distribution within the bone; this mineral density is linked to the bone's elastic modulus through an empirically derived power-law relationship, meaning that bones with higher mineral density are structurally stiffer.

Throughout this characterization of biological materials, the expected behavior is that the mechanical degradation of tendons and cartilage follows a power-law relationship relative to the cumulative number of loading cycles the tissue has endured: stiffness initially drops slowly, but the rate of decline accelerates as more cycles accumulate. When this drop in elastic modulus exceeds thirty percent of the healthy tissue's original value, the reduction ceases to be a minor variation and becomes clinically significant.

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