A theory of fatigue damage accumulation and repair in cortical bone

Abstract

An analysis is presented of the balance between the accumulation and repair of fatigue damage in osteonal bone. Fatigue damage is defined in terms of cracks seen histologically when precautions are taken to avoid preparation artifact. The rate of occurrence of such damage is assumed to be proportional to the product of applied peak-to-peak stress, raised to a power, and the loading frequency. The rate of damage repair is assumed to be proportional to the activation rate for osteonal remodeling, and to the mean cross-sectional area of the resulting osteons. An additional factor is introduced to account for the possibility that damage provokes nearby remodeling. The theory is used to compare data from previous experiments of two types: fatigue-to-failure, and studies in which histologically observable cracks are made more numerous by repetitive loading. The analysis shows that there is a measure of agreement between the results of the two kinds of experiments, but the current data are too limited, and the results are too dependent on the mode of loading, to adequately test the theory. However, the analysis provides a framework for designing experiments to more efficiently clarify the relationships between fatigue failure, cracks seen in histologic sections, and the rate at which such cracks are repaired by osteonal remodeling.

How and why humans grow thin skulls: Experimental evidence for systemic cortical robusticity

“…Bone tissue interacts dynamically with its mechanical environment. Force applied to a bone (quantified per unit area as stress, a), generates strain (deformation, E) whose cumulative effects, if sufficient in magnitude, can damage its microstructure and mechanical integrity (Carter, 1987;Martin andBurr, 1989, Martin, 1992.). Controlled experiments on both limb bones that form endochondrally (e.g., Woo et al, 1981;Lanyon, 1984, 1985) and facial bones that form intramembranously (e.g., Beecher, 1982, 1984;Bouvier and Hylander, 1981;Yamada and Kimmel, 1991) demonstrate that high levels of strains induce local osteoblastic responses that increase cortical bone mass.…”

Carbon Nanotubes in Bone Tissue Engineering

“…The nature of this dependence was first described in a semi-quantitative manner by Wolff (Wolff, 1886), who stated that remodeling of bone occurs in response to physical stresses or to the lack of themin that bone is deposited in sites subjected to stress and is resorbed from sites where there is not enough stress. Several mechanisms have been proposed to relate changes in mechanical loads to the adaptive responses in bone, including (among many others): piezoelectric and streaming potentials (Gjelsvik, 1973a,b;Pollack et al, 1984); mechanical fatigue microdamage (Frost,1960;Carter & Hayes, 1977;Carter & Cayler, 1983;1985;Martin, 1992;Prendergast & Taylor, 1994); and extra-cellular fluid pressure gradient effects on bone cells (Cowin et al, 1991;. Experimental evidence can be found in support of each of the above-mentioned mechanisms.…”

Using a Truss-Inspired Model with the Uniform Strength Optimization Theory to Predict Spongy Bone Geometry in Proximal Femur

“…The nature of this dependence was first described in a semiquantitative manner by Wolff [2], who stated that every change in function of a living bone is followed by adaptive changes in its internal architecture and shape. Several mechanisms have been proposed to relate changes in mechanical loads to the adaptive responses in bone, including: piezoelectric and streaming potentials [3,4], mechanical fatigue microdamage [5][6][7][8][9][10][11], and extra-cellular fluid pressure gradient effects on bone cells [12,13]. Experimental evidence can be found in support of each of the above-mentioned mechanisms.…”