Mechanism and microstructure based concept to predict skull fracture using a hybrid-experimental-modeling-computational approach.

Cellular and tissue-scale indent/impact thresholds for different mechanisms of functional impairments to the brain would be the preferred method to predict head injuries, but a comprehensive understanding of the dominant possible injury mechanisms under multiaxial stress-states and rates is currently not available. Until then, skull fracture could serve as an indication of head injury. Therefore the ability to predict the initiation of skull fracture through finite element simulation can serve as an in silico tool for assessing the effectiveness of various head protection scenarios. For this objective, skull fracture initiation was represented with a microstructurally-inspired, mechanism-based (MIMB) failure surface assuming three different dominant mechanisms of skull failure: each element, with deformation and failure properties selected based on its microstructure, was allowed to fail either in tension, compression, or shear, corresponding to clinical linear, depressed or penetrating shear-plug failure (fracture), respectively. Microstructure-inspired a priori values for the initiation threshold of each mechanism, obtained previously from uniaxial and simple-shear experiments, were iterated and optimized for the predicted load-displacement to represent that of the corresponding indentation experiment. Element-level failure enabled the visualization of the evolution of fracture by different mechanisms. The final crack pattern at the time of macroscopic (clinically-identifiable) injury was compared between the simulation and experiment obtained through 3D tomography. Even though the timing was slightly different, the simulated prediction represented remarkably well the experimental crack pattern before the appearance of the catastrophic unstable fast crack in the experiment, thus validating the implemented hybrid-experimental-modeling-computational (HEMC) concept as a tool to predict skull fracture initiation.

Implementation and validation of finite element model of skull deformation and failure response during uniaxial compression.

Numerical studies aimed at evaluating head injury due to externally applied loading can be made more biofidelic by incorporating nonlinear mechanism-based and microstructurally-inspired material models representing the mechanical response and fracture (failure or injury) of the human skull bone. Thus, incorporation of these mechanism-based models would increase the ability of simulations of mechanical impact to identify more realistic fracture-based injuries at clinical relevancy, such as linear (tensile), depressed (compressive), or penetration (shear). One of the challenges for accurate modeling of the mechanical response of the human skull is the intricate location dependent heterogeneous mesostructural arrangement of bone within the structure of the skull. Recently, a power-law relationship between the localized bone volume fraction (BVF) and modulus (E) within the human skull was developed based on quasi-static compression experiments. However, the parameters of the power-law were optimized and obtained using approximations which were not experimentally or computationally validated for the actual heterogeneous 3D bone structure. Here, a hybrid experimental-modeling-computational (HEMC) based concept was used to develop a microstructurally compatible detailed meso-scale finite element (FE) model of the heterogeneous microstructure of one of the human skull bone coupons previously used to derive the E-BVF relationship. Finite elements were mapped to the corresponding regions from microcomputed tomography images, and the BVF of each element was identified. Then, element-specific moduli were calculated from the E-BVF power relationship. The goal of the simulations was twofold: to assess the assumptions used to derive the E-BVF relationship from the linear regime of the experimental response, and also to model the subsequent deviation from linearity. Using the E-BVF relationship, the 3D simulation was able to match the experimentally measured global modulus to within 3%. After validating the E-BVF power law using the initial linear response, to develop and validate failure models, the following steps were completed. The subsequent deviation of the mechanical response from its initial linearity was assumed to be due to failure of elements either by compression or tension. Elemental microstructure-specific compressive and tensile failure thresholds (σf) for each element were modeled by BVF (fBV) power functional relationships of the form: [Formula: see text] MPa. The initial leading coefficients (σf,0) for compression and tension were derived from prior reported experimental work. Through incorporating element-level failure and then iterating the leading coefficients, the simulation was able to represent the nonlinearity of the stress-strain curve and its catastrophic failure in the experiment. Evolution of the measured non-uniform full-strain-fields on two surfaces of the coupon, showing the localized regions of failure, was compared between experiment and simulation, and was approximately similar, thus validating the developed HEMC procedure and failure models. The simulation methodology developed here allowed for identification of failure location within the skull coupon specimen, thereby providing a tool to predict the localized failure (fracture or injury) initiation within the human skull in FE simulations at larger length scales.

Multiscale response of the human skull to quasi-static compression.

Full thickness skull specimens were extracted from the human crania, with both the inner and outer surfaces intact. The BVF-morphology (bone volume fraction) of these specimens had been previously characterized in detail and reported, with high-resolution micro-computed tomography at ~5 µm resolution. A subset of these specimens was loaded in the direction normal to the outer surface in quasi-static compression. In contrast to many previous mechanical characterization studies of skulls, following two additional procedures were used in this study. (1) Fresh skull specimens were used, which were stored refrigerated before mechanical loading, instead of using embalmed or dried specimens. (2) Furthermore, using digital image correlation, non-contact full-field inhomogeneous strain measurements were made using the speckled specimen surfaces and the compression platens, also avoiding possible errors in strain measurements from machine compliance and due to irregularities in the loading surfaces of the specimen. The averaged far-field compressive mechanical response was obtained from these local full-field measurements on the composite bone specimens. Assuming a layered structure for the skull bone, using the local averaged full-field strain measurements of each layer, a power law was used to represent the relationship between initial mechanical response and the averaged BVF of the layers. Using the measured porosity maps of the rest of the non-compressed specimens, this relationship was used to predict the modulus-depth dependency of the skull bone and the variabilities associated with the structure. The mechanical properties and density as a function of the normalized thickness of the skull are presented for use in finite element simulations to model the skull with the desired degrees of complexities, also based on the region of action, depending on the goals of the computer simulation of the impact: either as a single homogenous layer, three-layer sandwich, multilayer heterogeneous or continuous elemental structure. In addition, a power law was derived relating the compressive failure strength and bone volume fraction (BVF) for the skull bone.

Influence of the mesostructure on the compressive mechanical response of adolescent porcine cranial bone.

The Göttingen minipig has been used as a surrogate in impact experiments designed to better understand the mechanisms by which mechanical loading induces traumatic brain injury (TBI). However, the relationship between mechanical response and structural morphology of the minipig cranium must be understood relative to the human skull in order to accurately scale any quantitative results, such as injury thresholds, from non-human TBI experiments to the human anatomy. In this study, bone specimens were dissected from the crania of adolescent Göttingen minipigs. These specimens were small cubes that contained the entire thickness of the skull. The microstructure of these skull specimens was quantified at the micron-length scale using micro-computed tomography (micro-CT). The skull was found to be highly porous near the skin-side surface and became less porous nearer the brain-side surface. The skull specimens were then loaded in quasi-static compression to obtain their mechanical response. The surface strain distribution on the specimen face was measured during loading using digital image correlation (DIC). The 2-D strain field formed a gradient of iso-strain bands along the thickness (depth) dimension from the skin-most to brain-most sides of the skull. The variation of the minipig microstructure along the thickness differed significantly from that of the adult human skull; thus the mechanical load transmission through the minipig skull is expected to be quite different from that of the human skull. The objective was to develop the methodology of relating the microstructure, as quantified by the bone volume fraction (BVF), to the mechanical response. The specimen was modeled by discretizing the depth dimension into a series of layers, which enabled the calibration of a power law relating the depth-dependent BVF to the depth-varying modulus. The relationship was used to predict moduli values for the adolescent minipig skull to provide updated, biofidelic parameters for finite element simulations at varying levels of complexity. Moreover, the methodology outlined in this paper can be applied to other skulls with different structural variations, such as the human.

Structural analysis of the frontal and parietal bones of the human skull.

Bone specimens were collected from the frontal and parietal bones of 4 adult, human skulls. The microstructure was characterized using microcomputed tomography (micro-CT) at about 6-µm resolution to map the change of porosity as a function of the depth, P(d), from the inner surface nearest to the brain to the outer surface nearest to the skin. A quantifiable method was developed using the measured P(d) to objectively distinguish between the three layers of the skull: the outer table, diploë , and inner table. The thickness and average porosity of each of the layers were then calculated from the measured porosity distributions, and a Gaussian function was fit to the P(d) curves. Morphological parameters were compared between the two bone types (frontal and parietal), while accounting for skull-to-skull variability. Parietal bones generally had a larger diploë accompanied by a thinner inner table. The arrangement of the porous vesicular structure within the outer table was also obtained with micro-CT scans with longer scan times, using enhanced parameters for higher resolution and lower noise in the images. From these scans, the porous structure of the bone appeared to be randomly arranged in the transverse plane, compared to the porous structure of the human femur, which is aligned in the loading direction.

The Multi-Axial Failure Response of Porcine Trabecular Skull Bone Estimated Using Microstructural Simulations.

The development of a multi-axial failure criterion for trabecular skull bone has many clinical and biological implications. This failure criterion would allow for modeling of bone under daily loading scenarios that typically are multi-axial in nature. Some yield criteria have been developed to evaluate the failure of trabecular bone, but there is a little consensus among them. To help gain deeper understanding of multi-axial failure response of trabecular skull bone, we developed 30 microstructural finite element models of porous porcine skull bone and subjected them to multi-axial displacement loading simulations that spanned three-dimensional (3D) stress and strain space. High-resolution microcomputed tomography (microCT) scans of porcine trabecular bone were obtained and used to develop the meshes used for finite element simulations. In total, 376 unique multi-axial loading cases were simulated for each of the 30 microstructure models. Then, results from the total of 11,280 simulations (approximately 135,360 central processing unit-hours) were used to develop a mathematical expression, which describes the average three-dimensional yield surface in strain space. Our results indicate that the yield strain of porcine trabecular bone under multi-axial loading is nearly isotropic and despite a spread of yielding points between the 30 different microstructures, no significant relationship between the yield strain and bone volume fraction is observed. The proposed yield equation has simple format and it can be implemented into a macroscopic model for the prediction of failure of whole bones.

Dynamic compressive response of bovine liver tissues.

This study aims to experimentally determine the strain rate effects on the compressive stress-strain behavior of bovine liver tissues. Fresh liver tissues were used to make specimens for mechanical loading. Experiments at quasi-static strain rates were conducted at 0.01 and 0.1 s(-1). Intermediate-rate experiments were performed at 1, 10, and 100 s(-1). High strain rate (1000, 2000, and 3000 s(-1)) experiments were conducted using a Kolsky bar modified for soft material characterization. A hollow transmission bar with semi-conductor strain gages was used to sense the weak forces from the soft specimens. Quartz-crystal force transducers were used to monitor valid testing conditions on the tissue specimens. The experiment results show that the compressive stress-strain response of the liver tissue is non-linear and highly rate-sensitive, especially when the strain rate is in the Kolsky bar range. The tissue stiffens significantly with increasing strain rate. The responses from liver tissues along and perpendicular to the liver surface were consistent, indicating isotropic behavior.

Dynamic and quasi-static compressive response of porcine muscle.

Research and application activities in impact biomechanics require dynamic response of biological tissues under high-rate loading. However, experimental difficulties have limited the characterization of soft tissues under such loading conditions. In this paper, we identify these technical challenges in dynamic compression experiments using a split Hopkinson pressure bar (SHPB) and present the remedies to overcome them. In order to subject the specimens to valid dynamic testing conditions, in addition to developing new pulse-shaping techniques and incorporating highly sensitive load-measuring transducers, annular thin-disc specimens radically different from regular solid specimens were used to minimize radial inertia effects that may overshadow the intrinsic material properties. By using this modified SHPB, the compressive stress-strain behavior of soft porcine muscle tissue was obtained along and perpendicular to the muscle fiber direction from quasi-static to dynamic strain rates. The results show that the non-linear compressive stress-strain responses in both directions are strongly strain-rate sensitive.