Relation between mechanical and densimetric properties to fractal dimension in human rib cortical bone.

BACKGROUND: Numerous prior studies hypothesized a power-law relationship (E∝ρα) between cortical bone Young's modulus (E) and density (ρ) with an exponent 2.3≤α≤3.0, that has not been previously justified in the literature on a theoretical level. Moreover, despite the fact microstructure have been extensively studied, the material correlate of Fractal Dimension (FD) as a descriptor of bone microstructure was not clear in previous studies. METHODS: This study examined the effect of mineral content and density on the mechanical properties of a large number of human rib cortical bone samples. The mechanical properties were calculated using Digital Image Correlation and uniaxial tensile tests. CT scans were used to calculate the Fractal Dimension (FD) of each specimen. For each specimen, the mineral (fmin), organic (forg) and water (fwat) weight fractions were determined. In addition, density was measured after a drying-and-ashing process. Then, Regression Analysis was employed to investigate the relationship between anthropometric variables, weight fractions, density and FD, as well as its impact on the mechanical properties. FINDINGS: Young's modulus exhibited a power-law relationship with an exponent of α>2.3 when using the conventional density (wet density), but α=2 when using dry density (desecated specimens). In addition, FD increases with decreasing cortical bone density. A significant relationship has been found between FD and density, whereby FD is correlated with the embedding of low density regions in cortical bone. INTERPRETATION: This study provides a new insight in the exponent value of the power-law relation between Young's Modulus and density, and relates bone behavior with the fragile fracture theory in ceramic materials. Moreover, the results suggest that Fractal Dimension is related to presence of low-density regions.

A strain rate dependent model with decreasing Young's Modulus for cortical human bone.

In the existing literature, some studies have observed an increase in the elastic modulus of human cortical bone with strain rate, which has been described as a consequence of the viscoelastic properties of the bone. However, these results contradict the findings of other studies, in which an independence or decrease of the elastic modulus with strain rate is observed, which could be explained by other non-viscoelastic mechanisms. This research studies the dynamic behavior of human cortical bone specimens and investigates their mechanical properties . A full and objective strain rate dependent model is proposed and used to describe the experimental results obtained from uniaxial tensile tests of twenty-one human rib cortical bone specimens from twelve male post mortem human subjects (average age of 68.5 ± 12.3 years). In addition, a general discussion of some families of viscoelastic models is given and the caution with which they should be used when dealing with complex materials such as bone. The main experimental finding is that in the range of strain rate analyzed (ε̇=0.10-0.60), there is a significant decrease in Young's modulus (E≈ 18 GPa forε̇=0.10s-1andE≈ 8 GPa forε̇=0.50s-1), which is not of viscoelastic origin. Moreover, the most frequently used viscoelastic models analyzed in this study predict how the elastic modulus should not vary markedly with strain rate for small strains. In fact, the observed behavior seems related to the findings of other researchers who observed that the microcraking damage depends on the strain rate in the same sense found in our work. This allows us to interpret the qualitative results as a consequence of the microcracking that takes place within the cortical bone, and not related to viscoelastic effects.

A stochastic model for soft tissue failure using acoustic emission data.

The strength of soft tissues is due mainly to collagen fibers. In most collagenous tissues, the arrangement of the fibers is random, but has preferred directions. The random arrangement makes it difficult to make deterministic predictions about the starting process of fiber breaking under tension. When subjected to tensile stress the fibers are progressively straighten out and then start to be stretched. At the beginning of fiber breaking, some of the fibers reach their maximum tensile strength and break down while some others remain unstressed (this latter fibers will assume then bigger stress until they eventually arrive to their failure point). In this study, a sample of human esophagi was subjected to a tensile breaking of fibers, up to the complete failure of the specimen. An experimental setup using Acoustic Emission to detect the elastic energy released is used during the test to detect the location of the emissions and the number of micro-failures per time unit. The data were statistically analyzed in order to be compared to a stochastic model which relates the level of stress in the tissue and the probability of breaking given the number of previously broken fibers (i.e. the deterioration in the tissue). The probability of a fiber breaking as the stretch increases in the tissue can be represented by a non-homogeneous Markov process which is the basis of the stochastic model proposed. This paper shows that a two-parameter model can account for the fiber breaking and the expected distribution for ultimate stress is a Fréchet distribution.