Probabilistic Finite Element Analysis of Human Rib Biomechanics: A Framework for Improved Generalizability.

In dynamic impact events, thoracic injuries often involve rib fractures, which are closely related to injury severity. Previous studies have investigated the behavior of isolated ribs under impact loading conditions, but often neglected the variability in anatomical shape and tissue material properties. In this study, we used probabilistic finite element analysis and statistical shape modeling to investigate the effect of population-wide variability in rib cortical bone tissue mechanical properties and rib shape on the biomechanical response of the rib to impact loading. Using the probabilistic finite element analysis results, a response surface model was generated to rapidly investigate the biomechanical response of an isolated rib under dynamic anterior-posterior load given the variability in rib morphometry and tissue material properties. The response surface was used to generate pre-fracture force-displacement computational corridors for the overall population and a population sub-group of older mid-sized males. When compared to the experimental data, the computational mean response had a RMSE of 4.28N (peak force 94N) and 6.11N (peak force 116N) for the overall population and sub-group respectively, whereas the normalized area metric when comparing the experimental and computational corridors ranged from 3.32% to 22.65% for the population and 10.90% to 32.81% for the sub-group. Furthermore, probabilistic sensitivities were computed in which the contribution of uncertainty and variability of the parameters of interest was quantified. The study found that rib cortical bone elastic modulus, rib morphometry and cortical thickness are the random variables that produce the largest variability in the predicted force-displacement response. The proposed framework offers a novel approach for accounting biological variability in a representative population and has the potential to improve the generalizability of findings in biomechanical studies.

Investigating the Impact of Blunt Force Trauma: A Probabilistic Study of Behind Armor Blunt Trauma Risk.

Evaluating Behind Armor Blunt Trauma (BABT) is a critical step in preventing non-penetrating injuries in military personnel, which can result from the transfer of kinetic energy from projectiles impacting body armor. While the current NIJ Standard-0101.06 standard focuses on preventing excessive armor backface deformation, this standard does not account for the variability in impact location, thorax organ and tissue material properties, and injury thresholds in order to assess potential injury. To address this gap, Finite Element (FE) human body models (HBMs) have been employed to investigate variability in BABT impact conditions by recreating specific cases from survivor databases and generating injury risk curves. However, these deterministic analyses predominantly use models representing the 50th percentile male and do not investigate the uncertainty and variability inherent within the system, thus limiting the generalizability of investigating injury risk over a diverse military population. The DoD-funded I-PREDICT Future Naval Capability (FNC) introduces a probabilistic HBM, which considers uncertainty and variability in tissue material and failure properties, anthropometry, and external loading conditions. This study utilizes the I-PREDICT HBM for BABT simulations for three thoracic impact locations-liver, heart, and lower abdomen. A probabilistic analysis of tissue-level strains resulting from a BABT event is used to determine the probability of achieving a Military Combat Incapacitation Scale (MCIS) for organ-level injuries and the New Injury Severity Score (NISS) is employed for whole-body injury risk evaluations. Organ-level MCIS metrics show that impact at the heart can cause severe injuries to the heart and spleen, whereas impact to the liver can cause rib fractures and major lacerations in the liver. Impact at the lower abdomen can cause lacerations in the spleen. Simulation results indicate that, under current protection standards, the whole-body risk of injury varies between 6 and 98% based on impact location, with the impact at the heart being the most severe, followed by impact at the liver and the lower abdomen. These results suggest that the current body armor protection standards might result in severe injuries in specific locations, but no injuries in others.

Region specific anisotropy and rate dependence of Göttingen minipig brain tissue.

Traumatic brain injury is a major cause of morbidity in civilian as well as military populations. Computational simulations of injurious events are an important tool to understanding the biomechanics of brain injury and evaluating injury criteria and safety measures. However, these computational models are highly dependent on the material parameters used to represent the brain tissue. Reported material properties of tissue from the cerebrum and cerebellum remain poorly defined at high rates and with respect to anisotropy. In this work, brain tissue from the cerebrum and cerebellum of male Göttingen minipigs was tested in one of three directions relative to axon fibers in oscillatory simple shear over a large range of strain rates from 0.025 to 250 s-1. Brain tissue showed significant direction dependence in both regions, each with a single preferred loading direction. The tissue also showed strong rate dependence over the full range of rates considered. Transversely isotropic hyper-viscoelastic constitutive models were fit to experimental data using dynamic inverse finite element models to account for wave propagation observed at high strain rates. The fit constitutive models predicted the response in all directions well at rates below 100 s-1, after which they adequately predicted the initial two loading cycles, with the exception of the 250 s-1 rate, where models performed poorly. These constitutive models can be readily implemented in finite element packages and are suitable for simulation of both conventional and blast injury in porcine, especially Göttingen minipig, models.

Differences in running biomechanics between young, healthy men and women carrying external loads.

During U.S. Army basic combat training (BCT), women are more prone to lower-extremity musculoskeletal injuries, including stress fracture (SF) of the tibia, with injury rates two to four times higher than those in men. There is evidence to suggest that the different injury rates are, in part, due to sex-specific differences in running biomechanics, including lower-extremity joint kinematics and kinetics, which are not fully understood, particularly when running with external load. To address this knowledge gap, we collected computed tomography images and motion-capture data from 41 young, healthy adults (20 women and 21 men) running on an instrumented treadmill at 3.0 m/s with loads of 0.0 kg, 11.3 kg, or 22.7 kg. Using individualized computational models, we quantified the running biomechanics and estimated tibial SF risk over 10 weeks of BCT, for each load condition. Across all load conditions, compared to men, women had a significantly smaller flexion angle at the trunk (16.9%-24.6%) but larger flexion angles at the ankle (14.0%-14.7%). Under load-carriage conditions, women had a larger flexion angle at the hip (17.7%-23.5%). In addition, women had a significantly smaller hip extension moment (11.8%-20.0%) and ankle plantarflexion moment (10.2%-14.3%), but larger joint reaction forces (JRFs) at the hip (16.1%-22.0%), knee (9.1%-14.2%), and ankle (8.2%-12.9%). Consequently, we found that women had a greater increase in tibial strain and SF risk than men as load increases, indicating higher susceptibility to injuries. When load carriage increased from 0.0 kg to 22.7 kg, SF risk increased by about 250% in women but only 133% in men. These results provide quantitative evidence to support the Army's new training and testing doctrine, as it shifts to a more personalized approach that shall account for sex and individual differences.

A comparative analysis of dimensionality reduction surrogate modeling techniques for full human body finite element impact simulations.

Fast-running surrogate computational models (simpler computational models) have been successfully used to replace time-intensive finite element models. However, it is unclear how well they perform in accurately and efficiently replicating complex, full human body finite element models. Here we survey several surrogate modeling techniques and assess their accuracy in predicting full strain fields of tissues of interest during a highly dynamic behind armor blunt trauma impact to the liver. We found that coupling dimensionality reduction on the high-dimensional output space (principal component analysis or autoencoders) with machine learning techniques (Gaussian Process Regression or multi-output neural networks) provides a framework capable of accurately and efficiently replacing complex full human body models. It was found that these surrogate models can successfully predict the strain fields (<10% average strain error) of select tissues during a nonlinear impact event but careful consideration should be given to element parsing and modeling technique.

Effect of stride length on the running biomechanics of healthy women of different statures.

BACKGROUND: Tibial stress fracture is a debilitating musculoskeletal injury that diminishes the physical performance of individuals who engage in high-volume running, including Service members during basic combat training (BCT) and recreational athletes. While several studies have shown that reducing stride length decreases musculoskeletal loads and the potential risk of tibial injury, we do not know whether stride-length reduction affects individuals of varying stature differently. METHODS: We investigated the effects of reducing the running stride length on the biomechanics of the lower extremity of young, healthy women of different statures. Using individualized musculoskeletal and finite-element models of women of short (N = 6), medium (N = 7), and tall (N = 7) statures, we computed the joint kinematics and kinetics at the lower extremity and tibial strain for each participant as they ran on a treadmill at 3.0 m/s with their preferred stride length and with a stride length reduced by 10%. Using a probabilistic model, we estimated the stress-fracture risk for running regimens representative of U.S. Army Soldiers during BCT and recreational athletes training for a marathon. RESULTS: When study participants reduced their stride length by 10%, the joint kinetics, kinematics, tibial strain, and stress-fracture risk were not significantly different among the three stature groups. Compared to the preferred stride length, a 10% reduction in stride length significantly decreased peak hip (p = 0.002) and knee (p < 0.001) flexion angles during the stance phase. In addition, it significantly decreased the peak hip adduction (p = 0.013), hip internal rotation (p = 0.004), knee extension (p = 0.012), and ankle plantar flexion (p = 0.026) moments, as well as the hip, knee, and ankle joint reaction forces (p < 0.001) and tibial strain (p < 0.001). Finally, for the simulated regimens, reducing the stride length decreased the relative risk of stress fracture by as much as 96%. CONCLUSIONS: Our results show that reducing stride length by 10% decreases musculoskeletal loads, tibial strain, and stress-fracture risk, regardless of stature. We also observed large between-subject variability, which supports the development of individualized training strategies to decrease the incidence of stress fracture.

Effects of Stature and Load Carriage on the Running Biomechanics of Healthy Men.

OBJECTIVE: Overuse musculoskeletal injuries, often precipitated by walking or running with heavy loads, are the leading cause of lost-duty days or discharge during basic combat training (BCT) in the U.S. military. The present study investigates the impact of stature and load carriage on the running biomechanics of men during BCT. METHODS: We collected computed tomography images and motion-capture data for 21 young, healthy men of short, medium, and tall stature (n = 7 in each group) running with no load, an 11.3-kg load, and a 22.7-kg load. We then developed individualized musculoskeletal finite-element models to determine the running biomechanics for each participant under each condition, and used a probabilistic model to estimate the risk of tibial stress fracture during a 10-week BCT regimen. RESULTS: Under all load conditions, we found that the running biomechanics were not significantly different among the three stature groups. However, compared to no load, a 22.7-kg load significantly decreased the stride length, while significantly increasing the joint forces and moments at the lower extremities, as well as the tibial strain and stress-fracture risk. CONCLUSION: Load carriage but not stature significantly affected the running biomechanics of healthy men. SIGNIFICANCE: We expect that the quantitative analysis reported here may help guide training regimens and reduce the risk of stress fracture.

Rate- and Region-Dependent Mechanical Properties of Göttingen Minipig Brain Tissue in Simple Shear and Unconfined Compression.

Traumatic brain injury (TBI), particularly from explosive blasts, is a major cause of casualties in modern military conflicts. Computational models are an important tool in understanding the underlying biomechanics of TBI but are highly dependent on the mechanical properties of soft tissue to produce accurate results. Reported material properties of brain tissue can vary by several orders of magnitude between studies, and no published set of material parameters exists for porcine brain tissue at strain rates relevant to blast. In this work, brain tissue from the brainstem, cerebellum, and cerebrum of freshly euthanized adolescent male Göttingen minipigs was tested in simple shear and unconfined compression at strain rates ranging from quasi-static (QS) to 300 s-1. Brain tissue showed significant strain rate stiffening in both shear and compression. Minimal differences were seen between different regions of the brain. Both hyperelastic and hyper-viscoelastic constitutive models were fit to experimental stress, considering data from either a single loading mode (unidirectional) or two loading modes together (bidirectional). The unidirectional hyper-viscoelastic models with an Ogden hyperelastic representation and a one-term Prony series best captured the response of brain tissue in all regions and rates. The bidirectional models were generally able to capture the response of the tissue in high-rate shear and all compression modes, but not the QS shear. Our constitutive models describe the first set of material parameters for porcine brain tissue relevant to loading modes and rates seen in blast injury.

A Strain Rate-Dependent Constitutive Model for Göttingen Minipig Cerebral Arteries.

Computational simulations of traumatic brain injury (TBI) are commonly used to advance understanding of the injury-pathology relationship, tissue damage thresholds, and design of protective equipment such as helmets. Both human and animal TBI models have developed substantially over recent decades, partially due to the inclusion of more detailed brain geometry and representation of tissues like cerebral blood vessels. Explicit incorporation of vessels dramatically affects local strain and enables researchers to investigate TBI-induced damage to the vasculature. While some studies have indicated that cerebral arteries are rate-dependent, no published experimentally based, rate-sensitive constitutive models of cerebral arteries exist. In this work, we characterize the mechanical properties of axially failed porcine arteries, both quasi-statically (0.01 s-1) and at high rate (>100 s-1), and propose a rate-sensitive model to fit the data. We find that the quasi-static and high-rate stress-stretch curves become significantly different (p < 0.05) above a stretch of 1.23. We additionally find a significant change in both failure stretch and stress as a result of strain rate. The stress-stretch curve is then modeled as a Holzapfel-Gasser-Ogden material, with a Prony series added to capture the effects of viscoelasticity. Ultimately, this paper demonstrates that rate dependence should be considered in the material properties of cerebral arteries undergoing high strain-rate deformations and provides a ready-to-use model for finite element implementation.

Cerebral Vasculature Influences Blast-Induced Biomechanical Responses of Human Brain Tissue.

Multiple finite-element (FE) models to predict the biomechanical responses in the human brain resulting from the interaction with blast waves have established the importance of including the brain-surface convolutions, the major cerebral veins, and using non-linear brain-tissue properties to improve model accuracy. We hypothesize that inclusion of a more detailed network of cerebral veins and arteries can further enhance the model-predicted biomechanical responses and help identify correlates of blast-induced brain injury. To more comprehensively capture the biomechanical responses of human brain tissues to blast-wave exposure, we coupled a three-dimensional (3-D) detailed-vasculature human-head FE model, previously validated for blunt impact, with a 3-D shock-tube FE model. Using the coupled model, we computed the biomechanical responses of a human head facing an incoming blast wave for blast overpressures (BOPs) equivalent to 68, 83, and 104 kPa. We validated our FE model, which includes the detailed network of cerebral veins and arteries, the gyri and the sulci, and hyper-viscoelastic brain-tissue properties, by comparing the model-predicted intracranial pressure (ICP) values with previously collected data from shock-tube experiments performed on cadaver heads. In addition, to quantify the influence of including a more comprehensive network of brain vessels, we compared the biomechanical responses of our detailed-vasculature model with those of a reduced-vasculature model and a no-vasculature model for the same blast-loading conditions. For the three BOPs, the predicted ICP values matched well with the experimental results in the frontal lobe, with peak-pressure differences of 4-11% and phase-shift differences of 9-13%. As expected, incorporating the detailed cerebral vasculature did not influence the ICP, however, it redistributed the peak brain-tissue strains by as much as 30% and yielded peak strain differences of up to 7%. When compared to existing reduced-vasculature FE models that only include the major cerebral veins, our high-fidelity model redistributed the brain-tissue strains in most of the brain, highlighting the importance of including a detailed cerebral vessel network in human-head FE models to more comprehensively account for the biomechanical responses induced by blast exposure.

The importance of modeling the human cerebral vasculature in blunt trauma.

BACKGROUND: Multiple studies describing human head finite element (FE) models have established the importance of including the major cerebral vasculature to improve the accuracy of the model predictions. However, a more detailed network of cerebral vasculature, including the major veins and arteries as well as their branch vessels, can further enhance the model-predicted biomechanical responses and help identify correlates to observed blunt-induced brain injury. METHODS: We used an anatomically accurate three-dimensional geometry of a 50th percentile U.S. male head that included the skin, eyes, sinuses, spine, skull, brain, meninges, and a detailed network of cerebral vasculature to develop a high-fidelity model. We performed blunt trauma simulations and determined the intracranial pressure (ICP), the relative displacement (RD), the von Mises stress, and the maximum principal strain. We validated our detailed-vasculature model by comparing the model-predicted ICP and RD values with experimental measurements. To quantify the influence of including a more comprehensive network of brain vessels, we compared the biomechanical responses of our detailed-vasculature model with those of a reduced-vasculature model and a no-vasculature model. RESULTS: For an inclined frontal impact, the predicted ICP matched well with the experimental results in the fossa, frontal, parietal, and occipital lobes, with peak-pressure differences ranging from 2.4% to 9.4%. For a normal frontal impact, the predicted ICP matched the experimental results in the frontal lobe and lateral ventricle, with peak-pressure discrepancies equivalent to 1.9% and 22.3%, respectively. For an offset parietal impact, the model-predicted RD matched well with the experimental measurements, with peak RD differences of 27% and 24% in the right and left cerebral hemispheres, respectively. Incorporating the detailed cerebral vasculature did not influence the ICP but redistributed the brain-tissue stresses and strains by as much as 30%. In addition, our detailed-vasculature model predicted strain reductions by as much as 28% when compared to current reduced-vasculature FE models that only include the major cerebral vessels. CONCLUSIONS: Our study highlights the importance of including a detailed representation of the cerebral vasculature in FE models to more accurately estimate the biomechanical responses of the human brain to blunt impact.

A 3-D Finite-Element Minipig Model to Assess Brain Biomechanical Responses to Blast Exposure.

Despite years of research, it is still unknown whether the interaction of explosion-induced blast waves with the head causes injury to the human brain. One way to fill this gap is to use animal models to establish "scaling laws" that project observed brain injuries in animals to humans. This requires laboratory experiments and high-fidelity mathematical models of the animal head to establish correlates between experimentally observed blast-induced brain injuries and model-predicted biomechanical responses. To this end, we performed laboratory experiments on Göttingen minipigs to develop and validate a three-dimensional (3-D) high-fidelity finite-element (FE) model of the minipig head. First, we performed laboratory experiments on Göttingen minipigs to obtain the geometry of the cerebral vasculature network and to characterize brain-tissue and vasculature material properties in response to high strain rates typical of blast exposures. Next, we used the detailed cerebral vasculature information and species-specific brain tissue and vasculature material properties to develop the 3-D high-fidelity FE model of the minipig head. Then, to validate the model predictions, we performed laboratory shock-tube experiments, where we exposed Göttingen minipigs to a blast overpressure of 210 kPa in a laboratory shock tube and compared brain pressures at two locations. We observed a good agreement between the model-predicted pressures and the experimental measurements, with differences in maximum pressure of less than 6%. Finally, to evaluate the influence of the cerebral vascular network on the biomechanical predictions, we performed simulations where we compared results of FE models with and without the vasculature. As expected, incorporation of the vasculature decreased brain strain but did not affect the predictions of brain pressure. However, we observed that inclusion of the cerebral vasculature in the model changed the strain distribution by as much as 100% in regions near the interface between the vasculature and the brain tissue, suggesting that the vasculature does not merely decrease the strain but causes drastic redistributions. This work will help establish correlates between observed brain injuries and predicted biomechanical responses in minipigs and facilitate the creation of scaling laws to infer potential injuries in the human brain due to exposure to blast waves.

Does Blast Exposure to the Torso Cause a Blood Surge to the Brain?

The interaction of explosion-induced blast waves with the torso is suspected to contribute to brain injury. In this indirect mechanism, the wave-torso interaction is assumed to generate a blood surge, which ultimately reaches and damages the brain. However, this hypothesis has not been comprehensively and systematically investigated, and the potential role, if any, of the indirect mechanism in causing brain injury remains unclear. In this interdisciplinary study, we performed experiments and developed mathematical models to address this knowledge gap. First, we conducted blast-wave exposures of Sprague-Dawley rats in a shock tube at incident overpressures of 70 and 130 kPa, where we measured carotid-artery and brain pressures while limiting exposure to the torso. Then, we developed three-dimensional (3-D) fluid-structure interaction (FSI) models of the neck and cerebral vasculature and, using the measured carotid-artery pressures, performed simulations to predict mass flow rates and wall shear stresses in the cerebral vasculature. Finally, we developed a 3-D finite element (FE) model of the brain and used the FSI-computed vasculature pressures to drive the FE model to quantify the blast-exposure effects in the brain tissue. The measurements from the torso-only exposure experiments revealed marginal increases in the peak carotid-artery overpressures (from 13.1 to 28.9 kPa). Yet, relative to the blast-free, normotensive condition, the FSI simulations for the blast exposures predicted increases in the peak mass flow rate of up to 255% at the base of the brain and increases in the wall shear stress of up to 289% on the cerebral vasculature. In contrast, our simulations suggest that the effect of the indirect mechanism on the brain-tissue-strain response is negligible (<1%). In summary, our analyses show that the indirect mechanism causes a sudden and abundant stream of blood to rapidly propagate from the torso through the neck to the cerebral vasculature. This blood surge causes a considerable increase in the wall shear stresses in the brain vasculature network, which may lead to functional and structural effects on the cerebral veins and arteries, ultimately leading to vascular pathology. In contrast, our findings do not support the notion of strain-induced brain-tissue damage due to the indirect mechanism.