Damien Subit

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.

A study of the pedestrian impact kinematics using finite element dummy models: the corridors and dimensional analysis scaling of upper-body trajectories

Pedestrian–vehicle impact experiments using cadavers have shown that factors such as vehicle shape and pedestrian anthropometry can influence pedestrian kinematics and injury mechanisms. Although a parametric study examining these factors could elucidate the complex relationships that govern pedestrian kinematics, it would be impractical with cadaver tests because of the relative expense involved in performing numerous experiments on subjects with varying anthropometry. On the other hand, finite element modelling represents a more feasible approach because numerous experiments can be conducted for a fraction of the expense. The current study examined the relationship between pedestrian anthropometry and front shape of a mid-size sedan using a PAM-CRASH model of the 50th-percentile male (50th M) Polar-II pedestrian dummy extensively validated against experimental data. To evaluate the influence of pedestrian anthropometry on response kinematics, scaled dummy models were developed on the basis of the weight and height of the 5th-percentile female (5th F), 50th-percentile female (50th F) and 95th-percentile male (95th M). Simulations of the 5th F, 50th F, 50th M, and 95th M Polar-II finite element models struck at 40 km/h by a mid-size sedan were used to generate trajectories of the head, upper thorax, mid-thorax and pelvis. In an effort to assess the validity of scaling techniques when interpreting trajectory data from vehicle–pedestrian crashes, the trajectories of the 5th F, 50th F and 95th M model were scaled to the 50th M and compared with those generated by the 50th M model. The results demonstrated non-linear behaviour of dummy kinematics that could not be accounted for with traditional dimensional analysis scaling techniques.

Microstructure of the ligament-to-bone attachment complex in the human knee joint

Clinical and experimental studies have shown that injuries in the human knee ligaments occur in the ligament midsubstance, at the transition between bone and ligament, and in the bone in the vicinity of the ligament-to-bone attachment site. Whereas ligament and bone have been thoroughly described, the way they connect to each other remains unclear. The goal of this study is to provide a description of the microstructure of the ligament-to-bone insertion, with the view of providing a mechanical model capable of predicting the injuries that occur at this insertion. The preparatory literature review showed that there was no description of the insertion microstructure for the human ligaments. The results found for human tendons and animal tendons/ligaments were used to lead the histological and electron - scanning and transmission - microscopy analysis. The posterior cruciate ligament (PCL), and the lateral collateral ligament (LCL) were sampled from one post mortem human subject. Slices were cut along the longitudinal direction of the ligaments, following the fibers direction. The histology analysis showed that the insertion has the same structure as reported in the literature: it is made of a mineralization front between calcified and uncalcified fibrocartilage, which is not crossed by the ligament fibers. The transmission electron microscopy analysis of the calcified fibrocartilage revealed a collagenous structure which has a direction drastically different from the direction of the ligament fibers. The mechanical function of the insertion was discussed and combined with the histological findings to hypothesize the microstructure of the insertion.

Fractal dimension and mechanical properties of human cortical bone.

Fractal dimension (FD) can be used to characterize microstructure of porous media, particularly bone tissue. The porous microstructure of cortical bone is observable in micro-CT (μCT) images. Estimations of fractal dimensions of μCT images of coupons of human cortical bone are obtained. The same samples were tested on a tensile test machine and Youngs modulus (YM) and Failure stress were obtained. When both types of measures were compared, a clear correlation was found (R=-81%, P<0.01). Youngs modulus of each sample and the FD of its μCT images are correlated. From the assumption that cortical bone is approximately a fractal set, a non-linear constitutive relation involving FD is obtained for YM. Experimental results show good agreement with this constitutive relation. Additional parameters in the non-linear relation between YM and FD have been estimated from experimental results and related to physical parameters.

A Parametric Study of Hard Tissue Injury Prediction Using Finite Elements: Consideration of Geometric Complexity, Subfailure Material Properties, CT-Thresholding, and Element Characteristics

Objective: The objectives of this study were to examine the axial response of the clavicle under quasistatic compressions replicating the body boundary conditions and to quantify the sensitivity of finite element–predicted fracture in the clavicle to several parameters. Methods: Clavicles were harvested from 14 donors (age range 14–56 years). Quasistatic axial compression tests were performed using a custom rig designed to replicate in situ boundary conditions. Prior to testing, high-resolution computed tomography (CT) scans were taken of each clavicle. From those images, finite element models were constructed. Factors varied parametrically included the density used to threshold cortical bone in the CT scans, the presence of trabecular bone, the mesh density, Youngs modulus, the maximum stress, and the element type (shell vs. solid, triangular vs. quadrilateral surface elements). Results: The experiments revealed significant variability in the peak force (2.41 ± 0.72 kN) and displacement to peak force (4.9 ± 1.1 mm), with age (p < .05) and with some geometrical traits of the specimens. In the finite element models, the failure force and location were moderately dependent upon the Youngs modulus. The fracture force was highly sensitive to the yield stress (80–110 MPa). Conclusion: Neither fracture location nor force was strongly dependent on mesh density as long as the element size was less than 5 × 5 mm2. Both the fracture location and force were strongly dependent upon the threshold density used to define the thickness of the cortical shell.

Development of a computational framework to adjust the pre-impact spine posture of a whole-body model based on cadaver tests data

A method was developed to adjust the posture of a human numerical model to match the pre-impact posture of a human subject. The method involves pulling cables to prescribe the position and orientation of the head, spine and pelvis during a simulation. Six postured models matching the pre-impact posture measured on subjects tested in previous studies were created from a human numerical model. Posture scalars were measured on pre- and after applying the method to evaluate its efficiency. The lateral leaning angle θL defined between T1 and the pelvis in the coronal plane was found to be significantly improved after application with an average difference of 0.1±0.1° with the PMHS (4.6±2.7° before application). This method will be applied in further studies to analyze independently the contribution of pre-impact posture on impact response using human numerical models.

Biomechanical properties of the costovertebral joint.

Proper modeling of the human trunk requires a quantitative assessment of the stiffness of the costovertebral joints. Twelve samples (adjacent thoracic vertebrae and one rib segment) were harvested from three subjects. The ribs were loaded in the cranial-caudal direction, the ventral-dorsal direction and in torsion around the cervical rib axis. The force applied to and the displacement of the loading point on the rib were measured and used to determine the moment-angle responses. Characteristic average curves and boundary curves containing the dataset were developed. The torsion response presented a range of motion--defined as the change in the angle for an applied moment varying from -0.1 to 0.1 Nm--of 16.9+/-6.8 degrees which is more than three times the range in cranial-caudal flexion and five times the range in ventral-dorsal flexion. Statistical tests showed a significant difference between these ranges of motion. Significant inter-subject variability was observed for the cranial-caudal flexion (p<0.05) while no intra-subject variability appeared. The characteristic moment-angle responses of the joints were well represented by third order polynomials (R(2)>0.9). This study expands and supplements the limited data available in the literature. Furthermore, it provides biomechanical data (closed-form moment-angle functions) that can be directly integrated into spine-ribcage models.

Investigating Pedestrian Kinematics with the Polar-II Finite Element Model

This paper is from the SAE World Congress & Exhibition, held in April 2007 in Detroit, Michigan, USA. Part of the Pedestrian Safety session, this paper reports on a study of pedestrian kinematics with the Polar-II Finite Element Model. The authors describe how earlier studies on pedestrian-vehicle impact kinematics used post-mortem human surrogates (PMHS) and determined that vehicle shape may influence pedestrian kinematics and injury mechanisms. The authors describe finite element (FE) modeling as a more feasible approach, since numerous experiments can be conducted with a significantly lower cost. The authors report on their study which used an FE model of the Polar-II pedestrian dummy to evaluate the influence of shifting body contact points with respect to vehicle geometry on impact kinematics. Multiple simulations were performed by moving the pedestrian vertically with respect to the vehicle reference frame. Another component of the study was undertaken to evaluate the contribution of the mass distribution with respect to vehicle geometry. In this part, simulations were performed where the center of gravity of the dummy was shifted around the baseline location. The authors discuss the results of this study which suggest a nonlinear sensitivity of response to changes in the body contact points with respect to vehicle structures, as well as a linear variation of upper body trajectories when the dummy center of gravity height was adjusted.

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.