Acoustic emission applied to stochastic modeling of microdamage in compact bone.

Exploring the stochastic intricacies of bone microstructure is a promising way to make progress on the practical issue of bone fracture. This study investigates the fracture of human complete ribs subjected to bending and using acoustic emission (AE) for microfailure detection. As the strain increases, the number of AE signals per unit of time rises until, beyond a certain threshold, an avalanche of signals occurs, indicating the aggregation of numerous microfailures into a macroscopic fracture. Since microfailures appear randomly throughout the bending test, and given the lack of a deterministic law and the random nature of microfailures during the bending test, we opted to develop a stochastic model to account for their occurrence within the irregular and random microstructure of the cortical bone. Notable discoveries encompass the significant correlation between adjusted parameters of the stochastic model and the total number of microfailures with anthropometric variables such as age and body mass index (BMI). The progression of microfailures with strain is significantly more pronounced with age and BMI, as measured by the rate of bone deterioration. In addition, the rate of microfailures is significantly impacted by BMI alone. It is also observed that the average energy of the identified AE events adheres to a precisely defined Pareto distribution for every specimen, with the principal exponent exhibiting a significant correlation with anthropometric variables. From a mathematical standpoint, the model can be described as a double Cox stochastic and explosive (coxplosive process) model. This further provides insight into the reason why the ribs of older individuals are considerably less resilient than those of younger individuals, breaking under a considerably lower maximum strain ( ε max ).

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 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).

Age effects on the mechanical behavior of human cerebral bridging veins.

BACKGROUND: It is well established that the probability of occurrence of acute subdural hematomas in traumatic situations increases with age, since the main cause of such hematomas is the mechanical failure of cerebral blood vessels known as bridging veins. This research aims to determine whether there is an effect of age on the mechanical properties of these cerebral vessels, because previous reported studies were conflicting. METHODS: This study used mechanical tests blue of cerebral bridging veins from post-mortem human subjects. In particular, a series of in vitro tensile tests were performed on a balanced sample of bridging veins from different human subjects. FINDINGS: The mechanical parameters measured from the tests were analyzed by means of regression analysis looking for age related effects. The results show that there is a significant effect on both the ultimate strength, maximum stress and strain that the specimens can withstand. The quantitative analysis shows reductions of nearly 50% in ultimate stress, and almost 35% in ultimate strain. INTERPRETATION: Mechanical deterioration of the mechanical strength of cerebral blood vessels seems to be a major factor involved in the increase of frequency of acute subdural hematoma in elderly people in a wide range of life-threatening traumatic situations.

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.