Influence of bone microstructure on the mechanical properties of skull cortical bone - A combined experimental and computational approach.

The strength and compliance of the dense cortical layers of the human skull have been examined since the beginning of the 20th century with the wide range in the observed mechanical properties attributed to natural biological variance. Since this variance may be explained by the difference in structural arrangement of bone tissue, micro-computed tomography (µCT) was used in conjunction with mechanical testing to study the relationship between the microstructure of human skull cortical coupons and their mechanical response. Ninety-seven bone samples were machined from the cortical tables of the calvaria of ten fresh post mortem human surrogates and tested in dynamic tension until failure. A linear response between stress and strain was observed until close to failure, which occurred at 0.6% strain on average. The effective modulus of elasticity for the coupons was 12.01 ± 3.28GPa. Porosity of the test specimens, determined from µCT, could explain only 51% of the variation of their effective elastic modulus. Finite element (FE) models of the tested specimens built from µCT images indicated that modeling the microstructural arrangement of the bone, in addition to the porosity, led to a marginal improvement of the coefficient of determination to 54%. Modulus for skull cortical bone for an element size of 50µm was estimated to be 19GPa at an average. Unlike the load bearing bones of the body, almost half of the variance in the mechanical properties of cortical bone from the skull may be attributed to differences at the sub-osteon (< 50µm) level. ANOVA tests indicated that effective failure stress and strain varied significantly between the frontal and parietal bones, while the bone phase modulus was different for the superior and inferior aspects of the calvarium. The micro FE models did not indicate any anisotropy attributable to the pores observable under µCT.

Experimental investigation of the effect of occupant characteristics on contemporary seat belt payout behavior in frontal impacts.

OBJECTIVE: The goal of this study was to investigate the influence of the occupant characteristics on seat belt force vs. payout behavior based on experiment data from different configurations in frontal impacts. METHODS: The data set reviewed consists of 58 frontal sled tests using several anthropomorphic test devices (ATDs) and postmortem human subjects (PMHS), restrained by different belt systems (standard belt, SB; force-limiting belt, FLB) at 2 impact severities (48 and 29 km/h). The seat belt behavior was characterized in terms of the shoulder belt force vs. belt payout behavior. A univariate linear regression was used to assess the factor significance of the occupant body mass or stature on the peak tension force and gross belt payout. RESULTS: With the SB, the seat belt behavior obtained by the ATDs exhibited similar force slopes regardless of the occupant size and impact severities, whereas those obtained by the PMHS were varied. Under the 48 km/h impact, the peak tension force and gross belt payout obtained by ATDs was highly correlated to the occupant stature (P =.03, P =.02) and body mass (P =.05, P =.04), though no statistical difference with the stature or body mass were noticed for the PMHS (peak force: P =.09, P =.42; gross payout: P =.40, P =.48). With the FLB under the 48 km/h impact, highly linear relationships were noticed between the occupant body mass and the peak tension force (R(2) = 0.9782) and between the gross payout and stature (R(2) = 0.9232) regardless of the occupant types. CONCLUSIONS: The analysis indicated that the PMHS characteristics showed a significant influence on the belt response, whereas the belt response obtained with the ATDs was more reproducible. The potential cause included the occupant anthropometry, body mass distribution, and relative motion among body segments specific to the population variance. This study provided a primary data source to understand the biomechanical interaction of the occupant with the restraint system. Further research is necessary to consider these effects in the computational studies and optimized design of the restraint system in a more realistic manner.

Biofidelity Corridors for Sternum Kinematics in Low-Speed Side Impacts.

OBJECTIVE: Field data show that side impact car crashes have become responsible for a greater proportion of the fatal crashes compared to frontal crashes, which suggests that the protection gained in frontal impact has not been matched in side impact. One of the reasons is the lack of understanding of the torso injury mechanisms in side impact. In particular, the deformation of the rib cage and how it affects the mechanical loading of the individual ribs have yet to be established. Therefore, the objective of this study was to characterize the ribcage deformation in side impacts by describing the kinematics of the sternum relative to the spine. METHODS: The 3D kinematics of the 1st and of the 5th or 6th thoracic vertebrae and of the sternum were obtained for three Post Mortem Human Subjects (PMHS) impacted laterally by a rigid wall traveling at 15 km/h. The experimental data were processed to express the kinematics of the sternum relative to the spine throughout the impact event. Methods were developed to interpolate the kinematics of the vertebrae for which experimental data were not available. RESULTS: The kinematics of the sternocostal junction for ribs 1 to 6 as well as the orientation of the sternum were expressed in the vertebra coordinate systems defined for each upper thoracic vertebra (T1 to T6). Corridors were designed for the motion of the sternum relative to each vertebra. In the experiments, the sternum moved upward for all rib levels (1 to 6), and away from the spine with an amplitude that increased with the decreasing rib level (from rib 1 to rib 6). None of the differences observed in the kinematics could be correlated to the occurrence of rib fractures. CONCLUSIONS: This study provides both qualitative and quantitative information for the ribcage skeletal kinematics in side impact. This data set provides the information required to better evaluate computational models of the thorax for side impact simulations. The corridors developed in this study provide new biofidelity targets for the impact response of the ribcage. This study contributes to augmenting the state of knowledge of the human chest deformation in side impact to better characterize the rib fracture mechanisms.

Variation in the human ribs geometrical properties and mechanical response based on X-ray computed tomography images resolution.

Computational models of the human body are commonly used for injury prediction in automobile safety research. To create these models, the geometry of the human body is typically obtained from segmentation of medical images such as computed tomography (CT) images that have a resolution between 0.2 and 1mm/pixel. While the accuracy of the geometrical and structural information obtained from these images depend greatly on their resolution, the effect of image resolution on the estimation of the ribs geometrical properties has yet to be established. To do so, each of the thirty-four sections of ribs obtained from a Post Mortem Human Surrogate (PMHS) was imaged using three different CT modalities: standard clinical CT (clinCT), high resolution clinical CT (HRclinCT), and microCT. The images were processed to estimate the rib cross-section geometry and mechanical properties, and the results were compared to those obtained from the microCT images by computing the 'deviation factor', a metric that quantifies the relative difference between results obtained from clinCT and HRclinCT to those obtained from microCT. Overall, clinCT images gave a deviation greater than 100%, and were therefore deemed inadequate for the purpose of this study. HRclinCT overestimated the rib cross-sectional area by 7.6%, the moments of inertia by about 50%, and the cortical shell area by 40.2%, while underestimating the trabecular area by 14.7%. Next, a parametric analysis was performed to quantify how the variations in the estimate of the geometrical properties affected the rib predicted mechanical response under antero-posterior loading. A variation of up to 45% for the predicted peak force and up to 50% for the predicted stiffness was observed. These results provide a quantitative estimate of the sensitivity of the response of the FE model to the resolution of the images used to generate it. They also suggest that a correction factor could be derived from the comparison between microCT and HRclinCT images to improve the response of the model developed based on HRclinCT images.

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.

Thoracic response targets for a computational model: a hierarchical approach to assess the biofidelity of a 50th-percentile occupant male finite element model.

Current finite element human thoracic models are typically evaluated against a limited set of loading conditions; this is believed to limit their capability to predict accurate responses. In this study, a 50th-percentile male finite element model (GHBMC v4.1) was assessed under various loading environments (antero-posterior rib bending, point loading of the denuded ribcage, omnidirectional pendulum impact and table top) through a correlation metric tool (CORA) based on linearly independent signals. The load cases were simulated with the GHBMC model and response corridors were developed from published experimental data. The model was found to be in close agreement with the experimental data both qualitatively and quantitatively (CORA ratings above 0.75) and the response of the thorax was overall deemed biofidelic. This study also provides relevant corridors and an objective rating framework that can be used for future evaluation of thoracic models.

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.

Understanding how pre-impact posture can affect injury outcome in side impact sled tests using a new tool for visualization of cadaver kinematics.

The effect of posture and subject-specific factors on injury outcome is an active field of research in injury biomechanics, in particular in automotive safety research where post-mortem human subjects (PMHS) are used as surrogates. Current PMHS tests routinely include acquisition of the subjects׳ geometry and kinematics. However, combining these two datasets to better understand the injury mechanism is still a challenge. This study investigated the connection between pre-impact posture and resulting injuries in six previously published side impact sled tests (three with a rigid wall and three with an airbag) by creating three-dimensional kinematic animations (3DKA) of the tests. The 3DKA allow qualitative assessment of parameters related to posture and their possible effect on injury outcome. The orientation of the struck scapula and the lateral leaning of the torso were identified as potentially significant parameters. The ranges of variation in these parameters were quantified and compared to the number of rib fractures for each subject: the data suggested a correlation, but there was insufficient data for a probabilistic analysis. The 3DKA were published with this study and are freely available.

The Contribution of Pre-impact Posture on Restrained Occupant Finite Element Model Response in Frontal Impact.

OBJECTIVE: The objective of this study was to discuss the influence of the pre-impact posture to the response of a finite element human body model (HBM) in frontal impacts. METHODS: This study uses previously published cadaveric tests (PMHS), which measured six realistic pre-impact postures. Seven postured models were created from the THUMS occupant model (v4.0): one matching the standard UMTRI driving posture as it was the target posture in the experiments, and six matching the measured pre-impact postures. The same measurements as those obtained during the cadaveric tests were calculated from the simulations, and biofidelity metrics based on signals correlation (CORA) were established to compare the response of the seven models to the experiments. RESULTS: The HBM responses showed good agreement with the PMHS responses for the reaction forces (CORA = 0.80 ± 0.05) and the kinematics of the lower part of the torso but only fair correlation was found with the head, the upper spine, rib strains (CORA= 0.50 ± 0.05) and chest deflections (CORA = 0.67 ± 0.08). All models sustained rib fractures, sternal fracture and clavicle fracture. The average number of rib fractures for all the models was 5.3 ± 1.0, lower than in the experiments (10.8 ± 9.0). Variation in pre-impact posture greatly altered the time histories of the reaction forces, deflections and the rib strains, mainly in terms of time delay, but no definite improvement in HBM response or injury prediction was observed. By modifying only the posture of the HBM, the variability in the impact response was found to be equivalent to that observed in the experiments. The postured HBM sustained from 4 to 8 rib fractures, confirming that the pre-impact posture influenced the injury outcome predicted by the simulation. CONCLUSIONS: This study tries to answer an important question: what is the effect of occupant posture on kinematics and kinetics. Significant differences in kinematics observed between HBM and PMHS suggesting more coupling between the pelvis and the spine for the models which makes the model response very sensitive to any variation in the spine posture. Consequently, the findings observed for the HBM cannot be extended to PMHS. Besides, pre-impact posture should be carefully quantified during experiments and the evaluation of HBM should take into account the variation in the predicted impact response due to the variation in the model posture.

The tolerance of the human body to automobile collision impact - a systematic review of injury biomechanics research, 1990-2009.

Road traffic injuries account for 1.3 million deaths per year world-wide. Mitigating both fatalities and injuries requires a detailed understanding of the tolerance of the human body to external load. To identify research priorities, it is necessary to periodically compare trends in injury tolerance research to the characteristics of injuries occurring in the field. This study sought to perform a systematic review on the last twenty years of experimental injury tolerance research, and to evaluate those results relative to available epidemiologic data. Four hundred and eight experimental injury tolerance studies from 1990-2009 were identified from a reference index of over 68,000 papers. Examined variables included the body regions, ages, and genders studied; and the experimental models used. Most (20%) of the publications studied injury to the spine. There has also been a substantial volume of biomechanical research focused on upper and lower extremity injury, thoracic injury, and injury to the elderly - although these injury types still occur with regularity in the field. In contrast, information on pediatric injury and physiological injury (especially in the central nervous system) remains lacking. Given their frequency of injury in the field, future efforts should also include improving our understanding of tolerances and protection of vulnerable road users (e.g., motorcyclists, pedestrians).

Variation of bone layer thicknesses and trabecular volume fraction in the adult male human calvarium.

The human calvarium is a sandwich structure with two dense layers of cortical bone separated by porous cancellous bone. The variation of the three dimensional geometry, including the layer thicknesses and the volume fraction of the cancellous layer across the population, is unavailable in the current literature. This information is of particular importance to mathematical models of the human head used to simulate mechanical response. Although the target geometry for these models is the median geometry of the population, the best attempt so far has been the scaling of a unique geometry based on a few median anthropometric measurements of the head. However, this method does not represent the median geometry. This paper reports the average three dimensional geometry of the calvarium from X-ray computed tomography (CT) imaging and layer thickness and trabecular volume fraction from micro CT (µCT) imaging of ten adult male post-mortem human surrogates (PMHS). Skull bone samples have been obtained and µCT imaging was done at a resolution of 30 µm. Monte Carlo simulation was done to estimate the variance in these measurements due to the uncertainty in image segmentation. The layer thickness data has been averaged over areas of 5mm(2). The outer cortical layer was found to be significantly (p < 0.01; Student's t test) thicker than the inner layer (median of thickness ratio 1.68). Although there was significant location to location difference in all the layer thicknesses and volume fraction measurements, there was no trend. Average distribution and the variance of these metrics on the calvarium have been shown. The findings have been reported as colormaps on a 2D projection of the cranial vault.

A computational biomechanical analysis to assess the trade-off between chest deflection and spine translation in side impact.

OBJECTIVES: The objective of this study is to evaluate how the impact energy is apportioned between chest deflection and translation of the vehicle occupant for various side impact conditions. METHODS: The Autoliv Total Human Model for Safety (modified THUMS v1.4) was subjected to localized lateral constant velocity impacts to the upper body. First, the impact tests performed on postmortem human subjects (PMHS) were replicated to evaluate THUMS biofidelity. In these tests, a 75-mm-tall flat probe impacted the thorax at 3 m/s at 3 levels (shoulder, upper chest, and mid-chest) and 3 angles (lateral, +15° posterolateral, and -15° anterolateral), for a stroke of 72 mm. Second, a parametric analysis was performed: the Autoliv THUMS response to a 250-mm impact was evaluated for varying impact levels (shoulder to mid-thorax by 50-mm increments), obliquity (0° [pure lateral] to +20° [posterior impacts] and to -20° [anterior impacts], by 5° steps), and impactor pitch (from 0 to 25° by 5° steps). A total of 139 simulations were run. The impactor force, chest deflection, spine displacement, and spine velocity were calculated for each simulation. RESULTS: The Autoliv THUMS biofidelity was found acceptable. Overall, the predictions from the model were in good agreement with the PMHS results. The worst ratings were observed for the anterolateral impacts. For the parametric analysis, maximum chest deflection (MCD) and maximum spine displacement (MSD) were found to consistently follow opposite trends with increasing obliquity. This trend was level dependent, with greater MCD (lower MSD) for the higher impact levels. However, the spine velocity for the 250-mm impactor stroke followed an independent trend that could not be linked to MCD or MSD. This suggests that the spine velocity, which can be used as a proxy for the thorax kinetic energy, needs to be included in the design parameters of countermeasures for side impact protection. CONCLUSION: The parametric analysis reveals a trade-off between the deformation of the chest (and therefore the risk of rib fracture) and the lateral translation of the spine: reducing the maximum chest deflection comes at the cost of increasing the occupant lateral displacement. The trade-off between MCD and MSD is location dependent, which suggests that an optimum point of loading on the chest for the action of a safety system can be found.

The Contribution of Pre-impact Spine Posture on Human Body Model Response in Whole-body Side Impact.

The objective of the study was to analyze independently the contribution of pre-impact spine posture on impact response by subjecting a finite element human body model (HBM) to whole-body, lateral impacts. Seven postured models were created from the original HBM: one matching the standard driving posture and six matching pre-impact posture measured for each of six subjects tested in previously published experiments. The same measurements as those obtained during the experiments were calculated from the simulations, and biofidelity metrics based on signals correlation were established to compare the response of HBM to that of the cadavers. HBM responses showed good correlation with the subject response for the reaction forces, the rib strain (correlation score=0.8) and the overall kinematics. The pre-impact posture was found to greatly alter the reaction forces, deflections and the strain time histories mainly in terms of time delay. By modifying only the posture of HBM, the variability in the impact response was found to be equivalent to that observed in the experiments performed with cadavers with different anthropometries. The patterns observed in the responses of the postured HBM indicate that the inclination of the spine in the frontal plane plays a major role. The postured HBM sustained from 2 to 5 bone fractures, including the scapula in some cases, confirming that the pre-impact posture influences the injury outcome predicted by the simulation.

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 Young's modulus (YM) and Failure stress were obtained. When both types of measures were compared, a clear correlation was found (R=-81%, P<0.01). Young's 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.

Response of the Worldwide Side Impact Dummy (WorldSID) to Localized Constant-Speed Impacts.

The objective of this study was to evaluate WorldSID constant-speed shoulder and thorax impact responses in terms of impact force, external and internal deflection (1D and 2D IR-Tracc response) for two velocities (1 m/s and 3 m/s), at three impact levels (shoulder, upper thorax and mid thorax) in three impact directions (lateral, +15° posterolateral, -15° anteraolateral). In addition, the impact force and external deflection were compared to previously published cadaver data. Each impact condition was repeated twice. A total of 42 tests were performed. The WorldSID's lowest peak impact force and external deflection were found for impact at shoulder level regardless of impact direction. Maximum force and deflection were found for impact at mid thorax. Comparison between WorldSID and PMHS showed similar external chest deflections for impacts at 3 m/s. The peak impact force response with respect to impact level was found to be reversed for the WorldSID compared to the PMHS, for which shoulder impact resulted in the highest peak force. External time history responses for the WorldSID compared to the one PMHS impacted at 1 m/s in lateral impact direction showed a significant difference in both timing and magnitude. External deflections at upper and mid thorax were approximately twice as high as the internal 1D deflection measured by the IR-Tracc. However, taking into account the rotation of the rib, the calculated 2D deflection response at the posterior impact direction was closer to the external deflection, and thus also to the PMHS deflection response at 3 m/s. These findings emphasize the need of 2D deflection measurement.

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.

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.

Response of the human torso to lateral and oblique constant-velocity impacts.

The objective of this study was to provide new biomechanical response data for the thorax with lateral and oblique loading, so as to support the development of safety systems for side impact protection that would offer the level of protection that has been achieved in frontal impact. Three male human cadavers were successively impacted by an impactor system delivering a constant velocity impact from the left and the right sides at three levels (shoulder, upper chest and mid-chest). Different impact directions were also chosen for each side: lateral, +15° posterolateral, -15° anterolateral. One subject was impacted at 1, 3 and 6 m/s whereas the other two subjects were impacted at 3 m/s only. A total of nineteen tests was performed. The impact force and the chest lateral deflection were measured using respectively a standard data acquisition system and also an optoelectronic stereophotogrammetric system (OSS). After each test, attempts were made to detect rib fractures by palpation, and a necropsy of the torso was performed after the tests series to document the injuries produced by all the tests. Overall, the peak impact force increased from the lowest impact level (mid-chest) to the highest (shoulder) and was found to be rate-sensitive. The force-deflection relationship was non linear for the shoulder impacts (stiffness increased with increasing deflection) whereas stiffness was nearly constant for the mid- and upper-chest impacts. The anterolateral impacts to the mid- and upper-chest generated more rib fractures than the other impact directions.

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.