Matthew Kindig

Rib fractures under anterior–posterior dynamic loads: Experimental and finite-element study

The purpose of this study was to investigate whether using a finite-element (FE) mesh composed entirely of hexahedral elements to model cortical and trabecular bone (all-hex model) would provide more accurate simulations than those with variable thickness shell elements for cortical bone and hexahedral elements for trabecular bone (hex-shell model) in the modeling human ribs. First, quasi-static non-injurious and dynamic injurious experiments were performed using the second, fourth, and tenth human thoracic ribs to record the structural behavior and fracture tolerance of individual ribs under anterior-posterior bending loads. Then, all-hex and hex-shell FE models for the three ribs were developed using an octree-based and multi-block hex meshing approach, respectively. Material properties of cortical bone were optimized using dynamic experimental data and the hex-shell model of the fourth rib and trabecular bone properties were taken from the literature. Overall, the reaction force-displacement relationship predicted by both all-hex and hex-shell models with nodes in the offset middle-cortical surfaces compared well with those measured experimentally for all the three ribs. With the exception of fracture locations, the predictions from all-hex and offset hex-shell models of the second and fourth ribs agreed better with experimental data than those from the tenth rib models in terms of reaction force at fracture (difference <15.4%), ultimate failure displacement and time (difference <7.3%), and cortical bone strains. The hex-shell models with shell nodes in outer cortical surfaces increased static reaction forces up to 16.6%, compared to offset hex-shell models. These results indicated that both all-hex and hex-shell modeling strategies were applicable for simulating rib responses and bone fractures for the loading conditions considered, but coarse hex-shell models with constant or variable shell thickness were more computationally efficient and therefore preferred.

Influence of mesh density, cortical thickness and material properties on human rib fracture prediction

The purpose of this paper was to investigate the sensitivity of the structural responses and bone fractures of the ribs to mesh density, cortical thickness, and material properties so as to provide guidelines for the development of finite element (FE) thorax models used in impact biomechanics. Subject-specific FE models of the second, fourth, sixth and tenth ribs were developed to reproduce dynamic failure experiments. Sensitivity studies were then conducted to quantify the effects of variations in mesh density, cortical thickness, and material parameters on the model-predicted reaction force-displacement relationship, cortical strains, and bone fracture locations for all four ribs. Overall, it was demonstrated that rib FE models consisting of 2000-3000 trabecular hexahedral elements (weighted element length 2-3mm) and associated quadrilateral cortical shell elements with variable thickness more closely predicted the rib structural responses and bone fracture force-failure displacement relationships observed in the experiments (except the fracture locations), compared to models with constant cortical thickness. Further increases in mesh density increased computational cost but did not markedly improve model predictions. A ±30% change in the major material parameters of cortical bone lead to a -16.7 to 33.3% change in fracture displacement and -22.5 to +19.1% change in the fracture force. The results in this study suggest that human rib structural responses can be modeled in an accurate and computationally efficient way using (a) a coarse mesh of 2000-3000 solid elements, (b) cortical shells elements with variable thickness distribution and (c) a rate-dependent elastic-plastic material model.

Biomechanical Response of Ribs Under Quasistatic Frontal Loading

Objective: The goal of the present study was to identify rib-level differences in fracture characteristics for individual ribs subjected to anterior–posterior loading. Methods: Twenty-seven individual ribs were extracted from levels 2 to 10 from 3 postmortem human subjects (2 females and one male) and subjected to anterior–posterior loading at a quasistatic (2 mm/s) loading rate. The ribs were placed in a fixture that provided a pinned boundary condition at each extremity, and each specimen was loaded to failure. Reaction force and strains on the internal and external cortical surfaces of the ribs were measured. Results: Rib 2 was found to be 3 to 4 times stiffer than rib 3, whereas all other ribs were comparable in stiffness to rib 3. Fracture forces, fracture displacement, and work to fracture showed no clear rib-level trends, although the young male subject consistently exhibited higher fracture force and work values than the elderly female subjects for a given rib level. The cortical strains on the external surface of the rib remained in tension during the loading, whereas the internal surface strains were in compression. The data from the present study were compared to a similar study performed at dynamic loading rates (1.43–1.85 m/s). The quasistatic tests exhibited lower peak force and greater normalized fracture displacement than the dynamic tests, though the work was comparable between the 2 studies. Conclusions: The present study is one of the few that focuses on testing the rib as an entire structure and can contribute to understanding of how the structural behavior of an individual rib contributes to the fracture tolerance of the overall thorax when undergoing frontal loading.

Morphology, distribution, mineral density and volume fraction of human calcified costal cartilage.

This study examines the properties of calcifying human costal cartilage and adjacent rib bone using qualitative and quantitative micro-computed tomography analysis. Calcifications are categorized with respect to location, microstructure, shape, and contiguity using a novel classification scheme and quantified in terms of mineral density, volume fraction, and length of infiltration from the costo-chondral junction (CCJ). Calcifications were present throughout the cartilage by location and ranged from small diffuse calcifications to nodes, rods, plates, and even large complex structures that exhibited a microstructural morphology similar to a cross-section of diaphysial bone, with a dense shell surrounding a trabecular core. Solid microstructure was most common for calcifications (44.5%), and the morphologies were found to vary with location, with rods and plates being most prevalent at the periphery (91.7% of all rods, 98.4% of all plates). The average mineral density of the calcifications over all locations and morphologies was 658.8±86.36, compared with 662.7±50.37 mgHA cm(-3) for the adjacent rib bone. The calcification volume fraction (6.54±4.71%) was less than the volume fraction of rib bone (21.62±6.44%). The length of contiguous calcification infiltrating from the CCJ into the costal cartilage, when present, was 19.21±11.65 mm. These changes in the costal cartilage should be considered in biomechanical models of the thorax since the presence, location, and morphology of the calcifications alter the material behavior of the costal cartilage, as well as the structural behavior of the entire rib.

Effect of intercostal muscle and costovertebral joint material properties on human ribcage stiffness and kinematics

Current finite element (FE) models of the human thorax are limited by the lack of local-level validation, especially in the ribcage. This study exercised an existing FE ribcage model for a 50th percentile male under quasi-static point loading and dynamic sternal loading. Both force-displacement and kinematic responses of the ribcage were compared against experimental data. The sensitivity of the model response to changes in the material properties of the costovertebral (CV) joints and intercostal muscles was assessed. The simulations found that adjustments to the CV joints tended to change the amount of rib rotation in the sagittal plane, while changes to the elastic modulus and thickness of the intercostal muscles tended to alter both the stiffness and the direction and magnitude of rib motions. This study can lend insight into the role that the material properties of these two thoracic structures play in the dynamics of the ribcage during a frontal loading condition.

Development and validation of a subject-specific finite element model of a human clavicle

This study aimed to develop and validate a finite element (FE) model of a human clavicle which can predict the structural response and bone fractures under both axial compression and anterior–posterior three-point bending loads. Quasi-static non-injurious axial compression and three-point bending tests were first conducted on a male clavicle followed by a dynamic three-point bending test to fracture. Then, two types of FE models of the clavicle were developed using bone material properties which were set to vary with the computed tomography image density of the bone. A volumetric solid FE model comprised solely of hexahedral elements was first developed. A solid-shell FE model was then created which modelled the trabecular bone as hexahedral elements and the cortical bone as quadrilateral shell elements. Finally, simulations were carried out using these models to evaluate the influence of variations in cortical thickness, mesh density, bone material properties and modelling approach on the biomechanical responses of the clavicle, compared with experimental data. The FE results indicate that the inclusion of density-based bone material properties can provide a more accurate reproduction of the force–displacement response and bone fracture timing than a model with uniform bone material properties. Inclusion of a variable cortical thickness distribution also slightly improves the ability of the model to predict the experimental response. The methods developed in this study will be useful for creating subject-specific FE models to better understand the biomechanics and injury mechanism of the clavicle.

Development of structural and material clavicle response corridors under axial compression and three point bending loading for clavicle finite element model validation

Clavicle injuries were frequently observed in automotive side and frontal crashes. Finite element (FE) models have been developed to understand the injury mechanism, although no clavicle loading response corridors yet exist in the literature to ensure the model response biofidelity. Moreover, the typically developed structural level (e.g., force-deflection) response corridors were shown to be insufficient for verifying the injury prediction capacity of FE model, which usually is based on strain related injury criteria. Therefore, the purpose of this study is to develop both the structural (force vs deflection) and material level (strain vs force) clavicle response corridors for validating FE models for injury risk modeling. 20 Clavicles were loaded to failure under loading conditions representative of side and frontal crashes respectively, half of which in axial compression, and the other half in three point bending. Both structural and material response corridors were developed for each loading condition. FE model that can accurately predict structural response and strain level provides a more useful tool in injury risk modeling and prediction. The corridor development method in this study could also be extended to develop corridors for other components of the human body.

Metatarsal Shape and Foot Type: A Geometric Morphometric Analysis

Planus and cavus foot types have been associated with an increased risk of pain and disability. Improving our understanding of the geometric differences between bones in different foot types may provide insights into injury risk profiles and have implications for the design of musculoskeletal and finite-element models. In this study, we performed a geometric morphometric analysis on the geometry of metatarsal bones from 65 feet, segmented from computed tomography (CT) scans. These were categorized into four foot types: pes cavus, neutrally aligned, asymptomatic pes planus, and symptomatic pes planus. Generalized procrustes analysis (GPA) followed by permutation tests was used to determine significant shape differences associated with foot type and sex, and principal component analysis was used to find the modes of variation for each metatarsal. Significant shape differences were found between foot types for all the metatarsals (p < 0.01), most notably in the case of the second metatarsal which showed significant pairwise differences across all the foot types. Analysis of the principal components of variation showed pes cavus bones to have reduced cross-sectional areas in the sagittal and frontal planes. The first (p = 0.02) and fourth metatarsals (p = 0.003) were found to have significant sex-based differences, with first metatarsals from females shown to have reduced width, and fourth metatarsals from females shown to have reduced frontal and sagittal plane cross-sectional areas. Overall, these findings suggest that metatarsal bones have distinct morphological characteristics that are associated with foot type and sex, with implications for our understanding of anatomy and numerical modeling of the foot.

Micromechanical modeling of calcifying human costal cartilage using the generalized method of cells.

Various tissues in the human body, including cartilage, are known to calcify with aging. There currently is no material model that accounts for the calcification in the costal cartilage, which could affect the overall structural response of the rib cage, and thus change the mechanisms and resistance to injury. The goal of this study is to investigate, through the development of a calcifying cartilage model, whether the calcification morphologies present in the costal cartilage change its effective material properties. A calcified cartilage material model was developed using the morphologies of calcifications obtained from microCT and the relaxed elastic modulus of the human costal cartilage obtained from indentation testing. The homogenized model of calcifying cartilage found that calcifications alter the effective material behavior of the cartilage, and this effect is highly dependent on the microstructural connectivity of the calcification. Calcifications which are not contiguous with the rib bone and constitute 0-18% of the cartilage volume increase the effective elastic modulus from its baseline value of 5MPa to up to 8MPa. Calcifications which are attached to the rib bone, which typically constitute 18-25% of the cartilage volume, result in effective moduli of 20-66MPa, depending on the microstructure, and introduce marked anisotropy into the material. The calcifying cartilage model developed in this study can be incorporated into biomechanical models of the aging thorax to better understand how calcifications in the aging thorax affect the structural response of the rib cage.

Structural response and strain patterns of isolated ribs under lateral loading

Efforts to mitigate thoracic injury under lateral impact require an understanding of the structural and fracture characteristics of individual ribs under lateral loading. While a number of studies have loaded segments of rib under three-point bending, this study is the first to investigate lateral loading onto entire ribs. Fifteen individual ribs were extracted, positioned upright and a lateral displacement at 1 m/sec was applied. Displacements at the time of fracture were relatively constant across rib levels at 18.3 ± 3.7 mm. Fracture forces ranged from 27 N to 270 N at the anterior extremity and 103 N to 326 N at the posterior extremity; this was also insensitive to rib number. The strain gages indicated that the point immediately opposite the loader on the ribs internal surface experienced the highest tensile strains, while elsewhere the internal surface was in compression and the external surface was in tension. This structural-level rib characterisation can help to better understand the mechanisms of thoracic injury under lateral impact.