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 probabilistic model for murder weapon identification using stab-marks in human ribs.

The aim of this article is to provide a scientific and statistical basis to identify the murder weapon in stabbing cases from the geometric characteristics of the stab-marks left on human ribs. For this purpose, a quantitative predictive model is developed, based on geometric measurements of the stab-mark and its location along the rib. A general method based on Bayesian inference and probabilities is used for the model development, rather than a deterministic model given its inability in certain occasions to identify the murder weapon. Following the process explained in this article to collect the stab-mark information required, the complete probabilistic model exposed attained a high accuracy in the identification of the murder weapon between two macroscopically identical blades with a microscopic alteration in one of them (more than 90% of correct identification is achieved).

Traumatic brain injury in pedestrian-vehicle collisions: Convexity and suitability of some functionals used as injury metrics.

BACKGROUND AND OBJECTIVE: Abrupt accelerations or decelerations can cause large strain in brain tissues and, consequently, different forms of Traumatic Brain Injury (TBI). In order to predict the effect of the accelerations on the soft tissues of the brain, many different injury metrics have been proposed (typically, an injury metric is a real valued functional of the accelerations). The objective of this article is to make a formal and empirical comparison, in order to identify general criteria for reasonable injury metrics, and propose a general guideline to avoid ill-proposed injury metrics. METHODS: A medium-sized sample of vehicle-pedestrian collisions, from Post Mortem Human Subject (PMHS) tests, is analyzed. A statistical study has been conducted in order to determine the discriminant power of the usual metrics. We use Principal Component Analysis to reduce dimensionality and to check consistency among the different metrics. In addition, this article compares the mathematical properties of some of these functionals, trying to identify the desirable properties that any of those functionals needs to fulfill in order to be useful for optimization. RESULTS: We have found a pair-wise consistency of all the currently used metrics (any two injury metrics are always positively related). In addition, we observed that two independent principal factors explain about 72.5% of the observed variance among all collision tests. This is remarkable because it indicates that despite high number of different injury metrics, a reduced number of variables can explain the results of all these metrics. With regard to the formal properties, we found that essentially all injury mechanisms can be accounted by means of scalable, differentiable and convex functionals (we propose to call minimization suitable injury metric any metric having these three formal properties). In addition three useful functionals, usable as injury metrics, are identified on the basis of the empirical comparisons. CONCLUSIONS: The commonly used metrics are highly consistent, but also highly redundant. Formal minimal conditions of a reasonable injury metric has been identified. Future proposals of injury metrics can benefit from the results of this study.

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.

A microcontinuum model for mechanical properties of esophageal tissue: experimental methodology and constitutive analysis.

Accurate material properties of tissues are a key factor for the improvement of medical procedures and treatments. Experimental data are essential in order to formulate and validate a useful constitutive model for predicting the mechanical behavior of tissues in these procedures. This study develops a comprehensive experimental protocol at multiple length scale levels in order to obtain stress-strain curves for esophagus tissue. This paper compares two different models: a conventional, non-linear elastic model, and a microcontinuum model based on fiber rearrangement. Also, a detailed description of the experimental procedure is provided. While the focus was on esophageal tissues, the experimental procedure and microcontinuum are considered widely applicable to other samples of soft tissue.

Minimization of analytical injury metrics for head impact injuries.

OBJECTIVE: To compare the predictions of the head injury criterion (HIC), currently used to predict the risk of traumatic brain injury in frontal vehicle impact and pedestrian impact tests, with the predictions of other empirical and analytical injury metrics. METHODS: The appropriateness of different criteria relative to injury metrics derived from a head finite element (FE) model is investigated for different deceleration pulses in this research. Empirical injury metrics are computed by direct calculation for different analyzed pulses. In addition, for each pulse full FE model simulations of a complete human head were performed by means of the SIMon model. The computations are used to calculate the analytical injury metrics. RESULTS: This article shows that an optimal head deceleration curve based on HIC does not minimize other analytical injury metrics. The results obtained in this study suggest that the HIC criterion does not necessarily provide the same severity ranking for different external loadings to the head as the injury metrics derived from the FE models. CONCLUSION: Countermeasures designed based only on HIC could differ significantly from those based on analytical injury measures computed by FE models. The use of multiple injury metrics is recommended given that no scalar measure seems to be positively and strongly correlated with relevant injury metrics.