Brain strain uncertainty due to shape variation in and simplification of head angular velocity profiles

Head angular velocity, instead of acceleration, is more predictive of brain strains. Surprisingly, no study exists that investigates how shape variation in angular velocity profiles affects brain strains, beyond characteristics such as peak magnitude and impulse duration. In this study, we evaluated brain strain uncertainty due to variation in angular velocity profiles and further compared with that resulting from simplifying the profiles into idealized shapes. To do so, we used reconstructed head impacts from American National Football League for shape extraction and simulated head uniaxial coronal rotations from onset to full stop. The velocity profiles were scaled to maintain an identical peak velocity magnitude and duration in order to isolate the shape for investigation. Element-wise peak maximum principal strains from 44 selected impacts were obtained. We found that the shape of angular velocity profile could significantly affect brain strain magnitude (e.g., percentage difference of 4.29–17.89 % in the whole brain relative to the group average, with cumulative strain damage measure (CSDM) uncertainty range of 23.9 %) but not pattern (correlation coefficient of 0.94–0.99). Strain differences resulting from simplifying angular velocity profiles into idealized shapes were largely within the range due to shape variation, in both percentage difference and CSDM (signed difference of 3.91 % on average, with a typical range of 0–6 %). These findings provide important insight into the uncertainty or confidence in the performance of kinematics-based injury metrics. More importantly, they suggest the feasibility to simplify head angular velocity profiles into idealized shapes, at least within the confinements of the profiles evaluated, to enable real-time strain estimation via pre-computation in the future.     

Influence of the crash pulse shape on the peak loading and the injury tolerance levels of the neck in in vitro low-speed side-collisions

The aim of the present in vitro study was to investigate the effect of the crash pulse shape on the peak loading and the injury tolerance levels of the human neck. In a custom-made acceleration apparatus 12 human cadaveric cervical spine specimens, equipped with a dummy head, were subjected to a series of incremental side accelerations. While the duration of the acceleration pulse of the sled was kept constant at 120 ms, its shape was varied: Six specimens were loaded with a slowly increasing pulse, i.e. a low loading rate, the other six specimens with a fast increasing pulse, i.e. a high loading rate. The loading of the neck was quantified in terms of the peak linear and angular acceleration of the head, the peak shear force and bending moment of the lower neck and the peak translation between head and sled. The shape of the acceleration curve of the sled only seemed to influence the peak translation between head and sled but none of the other four parameters. The neck injury tolerance level for the angular acceleration of the head and for the bending moment of the lower neck was almost identical for both, the high and the low loading rate. In contrast, the injury tolerance level for the linear acceleration of the head and for the shear force of the lower neck was slightly higher for the low loading rate as compared to the high loading rate. For the translation between head and sled this difference was even statistically significant. Thus, if the shape of the crash pulse is not known, solely the peak bending moment of the lower neck and the peak angular acceleration of the head seem to be suitable predictors for the neck injury risk but not the peak shear force of the lower neck, the peak linear acceleration of the head and the translation between head and thorax.     

Protective capacity of an ice hockey goaltender helmet for three events associated with concussion

The purpose of this study was to assess the protective capacity of an ice hockey goaltender helmet for three concussive impact events. A helmeted and unhelmeted headform was used to test three common impact events in ice hockey (fall, puck impacts and shoulder collisions). Peak linear acceleration, rotational acceleration and rotational velocity as well as maximum principal strain and von Mises stress were measured for each impact condition. The results demonstrated the tested ice hockey goaltender helmet was well designed to manage fall and puck impacts but does not consistently protect against shoulder collisions and an opportunity may exist to improve helmet designs to better protect goaltenders from shoulder collisions.     

Influence of angular acceleration-deceleration pulse shapes on regional brain strains

Recognizing the association of angular loading with brain injuries and inconsistency in previous studies in the application of the biphasic loads to animal, physical, and experimental models, the present study examined the role of the acceleration-deceleration pulse shapes on region-specific strains. An experimentally validated two-dimensional finite element model representing the adult male human head was used. The model simulated the skull and falx as a linear elastic material, cerebrospinal fluid as a hydrodynamic material, and cerebrum as a linear viscoelastic material. The angular loading matrix consisted coronal plane rotation about a center of rotation that was acceleration-only (4.5 ms duration, 7.8 krad/s/s peak), deceleration-only (20 ms, 1.4 krad/s/s peak), acceleration-deceleration, and deceleration-acceleration pulses. Both biphasic pulses had peaks separated by intervals ranging from 0 to 25 ms. Principal strains were determined at the corpus callosum, base of the postcentral sulcus, and cerebral cortex of the parietal lobe. The cerebrum was divided into 17 regions and peak values of average maximum principal strains were determined. In all simulations, the corpus callosum responded with the highest strains. Strains were the least under all simulations in the lower parietal lobes. In all regions peak strains were the same for both monophase pulses suggesting that the angular velocity may be a better metric than peak acceleration or deceleration. In contrast, for the biphasic pulse, peak strains were region- and pulse-shape specific. Peak values were lower in both biphasic pulses when there was no time separation between the pulses than the corresponding monophase pulse. Increasing separation time intervals increased strains, albeit non-uniformly. Acceleration followed by deceleration pulse produced greater strains in all regions than the other form of biphasic pulse. Thus, pulse shape appears to have an effect on regional strains in the brain.     

Peak linear and rotational acceleration magnitude and duration effects on maximum principal strain in the corpus callosum for sport impacts

Concussion has been linked to the presence of injurious strains in the brain tissues. Research investigating severe brain injury has reported that strains in the brain may be affected by two parameters: magnitude of the acceleration, and duration of that acceleration. However, little is known how this relationship changes in terms of creating risk for brain injury for magnitudes and durations of acceleration common in sporting environments. This has particular implications for the understanding and prevention of concussive risk of injury in sporting environments. The purpose of this research was to examine the interaction between linear and rotational acceleration and duration on maximum principal strain in the brain tissues for loading conditions incurred in sporting environments. Linear and rotational acceleration loading curves of magnitudes and durations similar to those from impact in sport were used as input to the University College Brain Trauma Model and maximum principal strain (MPS) was measured for the different curves. The results demonstrated that magnitude and duration do have an effect on the strain incurred by the brain tissue. As the duration of the acceleration increases, the magnitude required to achieve strains reflecting a high risk of concussion decreases, with rotational acceleration becoming the dominant contributor. The magnitude required to attain a magnitude of MPS representing risk of brain injury was found to be as low as 2500 rad/s² for impacts of 10–15 ms; indicating that interventions to reduce the risk of concussion in sport must consider the duration of the event while reducing the magnitude of acceleration the head incurs.     

Subject-specific finite element models implementing a maximum principal strain criterion are able to estimate failure risk and fracture location on human femurs tested in vitro

No agreement on the choice of the failure criterion to adopt for the bone tissue can be found in the literature among the finite element studies aiming at predicting fracture risk of bones. The use of stress-based criteria seems to prevail on strain-based ones, while basic bone biomechanics suggest using strain parameters to describe failure. The aim of the present combined experimental-numerical study was to verify, using subject-specific finite element models able to accurately predict strains, if a strain-based failure criterion could identify the failure patterns of bones. Three cadaver femurs were CT-scanned and subsequently fractured in a clinically relevant single-stance loading scenario. Load-displacement curves and high-speed movies were acquired to define the failure load and the location of fracture onset, respectively. Subject-specific finite element models of the three femurs were built from CT data following a validated procedure. A maximum principal strain criterion was implemented in the finite element models, and two stress-based criteria selected for comparison. The failure loads measured were applied to the models, and the computed risks of fracture were compared to the results of the experimental tests. The proposed principal strain criterion managed to correctly identify the level of failure risk and the location of fracture onset in all the modelled specimens, while Von Mises or maximum principal stress criteria did not give significant information. A maximum principal strain criterion can thus be defined a suitable candidate for the in vivo risk factor assessment on long bones.     

A modified human head model for the study of impact head injury

A recently published finite element (FE) head model is modified to consider the viscoelasticity of the meninges, the spongy and compact bone in the skull. The cerebrospinal fluid (CSF) is simulated explicitly as a hydrostatic fluid by using a surface-based fluid modelling method, which allows fluid and structure interaction. It is found that the modified model yields smoother pressure responses in a head impact simulation. The baseline model underestimated the peak von Mises stress in the brain by 15% and the peak principal stress in the skull by 33%. The increase in the maximum principal stress in the skull is mainly caused by the updation of the material's viscoelasticity, and the change in the maximum von Mises stress in the brain is mainly caused by the improvement of the CSF simulation. The study shows that the viscoelasticity of the head tissue should be considered, and that the CSF should be modelled as a fluid, when using FE analysis to study head injury due to impact.     

Head kinematics in mini-sled tests of foam padding: relevance of linear responses from free motion headform (FMH) testing to head angular responses

The revised Federal Motor Vehicle Safety Standard (FMVSS) No. 201 specifies that the safety performance of vehicle upper interiors is determined from the resultant linear acceleration response of a free motion headform (FMH) impacting the interior at 6.7 m/s. This study addresses whether linear output data from the FMH test can be used to select an upper interior padding that decreases the likelihood of rotationally induced brain injuries. Using an experimental setup consisting of a Hybrid III head-neck structure mounted on a mini-sled platform, sagittal plane linear and angular head accelerations were measured in frontal head impacts into foam samples of various stiffness and density with a constant thickness (51 mm) at low (approximately 5.0 m/s), intermediate (approximately 7.0 m/s), and high (approximately 9.6 m/s) impact speeds. Provided that the foam samples did not bottom out, recorded peak values of angular acceleration and change in angular velocity increased approximately linearly with increasing peak resultant linear acceleration and value of the Head Injury Criterion (HIC36). The results indicate that the padding that produces the lowest possible peak angular acceleration and peak change in angular velocity without causing high peak forces is the one that produces the lowest possible HIC36 without bottoming out in the FMH test.     

A modified human head model for the study of impact head injury

A recently published finite element (FE) head model is modified to consider the viscoelasticity of the meninges, the spongy and compact bone in the skull. The cerebrospinal fluid (CSF) is simulated explicitly as a hydrostatic fluid by using a surface-based fluid modelling method, which allows fluid and structure interaction. It is found that the modified model yields smoother pressure responses in a head impact simulation. The baseline model underestimated the peak von Mises stress in the brain by 15% and the peak principal stress in the skull by 33%. The increase in the maximum principal stress in the skull is mainly caused by the updation of the material's viscoelasticity, and the change in the maximum von Mises stress in the brain is mainly caused by the improvement of the CSF simulation. The study shows that the viscoelasticity of the head tissue should be considered, and that the CSF should be modelled as a fluid, when using FE analysis to study head injury due to impact.     

Influence of bicortical techniques in internal connection placed in premaxillary area by 3D finite element analysis

The aim of study was to evaluate the stress distribution in implant-supported prostheses and peri-implant bone using internal hexagon (IH) implants in the premaxillary area, varying surgical techniques (conventional, bicortical and bicortical in association with nasal floor elevation), and loading directions (0°, 30° and 60°) by three-dimensional (3D) finite element analysis. Three models were designed with Invesalius, Rhinoceros 3D and Solidworks software. Each model contained a bone block of the premaxillary area including an implant (IH, Ø4 × 10 mm) supporting a metal-ceramic crown. 178 N was applied in different inclinations (0°, 30°, 60°). The results were analyzed by von Mises, maximum principal stress, microstrain and displacement maps including ANOVA statistical test for some situations. Von Mises maps of implant, screws and abutment showed increase of stress concentration as increased loading inclination. Bicortical techniques showed reduction in implant apical area and in the head of fixation screws. Bicortical techniques showed slight increase stress in cortical bone in the maximum principal stress and microstrain maps under 60° loading. No differences in bone tissue regarding surgical techniques were observed. As conclusion, non-axial loads increased stress concentration in all maps. Bicortical techniques showed lower stress for implant and screw; however, there was slightly higher stress on cortical bone only under loads of higher inclinations (60°).     

Finite element modelling of equestrian helmet impacts exposes the need to address rotational kinematics in future helmet designs

Jockey head injuries, especially concussions, are common in horse racing. Current helmets do help to reduce the severity and incidences of head injury, but the high concussion incidence rates suggest that there may be scope to improve the performance of equestrian helmets. Finite element simulations in ABAQUS/Explicit were used to model a realistic helmet model during standard helmeted rigid headform impacts and helmeted head model University College Dublin Brain Trauma Model (UCDBTM) impacts.

Current helmet standards for impact determine helmet performance based solely on linear acceleration. Brain injury-related values (stress and strain) from the UCDBTM showed that a performance improvement based on linear acceleration does not imply the same improvement in head injury-related brain tissue loads. It is recommended that angular kinematics be considered in future equestrian helmet standards, as angular acceleration was seen to correlate with stress and strain in the brain.     

Mechanical significance of femoral head trabecular bone structure in Loris and Galago evaluated using micromechanical finite element models

Work on the interspecific and intraspecific variation of trabecular bone in the proximal femur of primates demonstrates important architectural variation between animals with different locomotor behaviors. This variation is thought to be related to the processes of bone adaptation whereby bone structure is optimized to the mechanical environment. Micromechanical finite element models were created for the proximal femur of the leaping Galago senegalensis and the climbing and quadrupedal Loris tardigradus by converting bone voxels from high-resolution X-ray computed tomography scans of the femoral head to eight-noded brick elements. The resulting models had approximately 1.8 million elements each. Loading conditions representing takeoff phase of a leap and more generalized load orientations were applied to the models, and the models were solved using the iterative "row-by-row" matrix-vector multiplication algorithm. The principal strain and Von Mises stress results for the leaping model were similar for both species at each load orientation. Similar hip joint reaction forces in the range of 4.9 x to 12 x body weight were calculated for both species under each loading condition, but the hip reaction values estimated for Loris were higher than predicted based on locomotor behavior. These results suggest that functional adaptation to hip joint loading may not fully explain the differences in femoral head trabecular bone structure in Galago and Loris. The finite element method represents a unique and useful tool for analyzing the functional adaptation of trabecular bone in a diversity of animals and for reconstructing locomotor behavior in extinct taxa.     

The influence of impact force redistribution and redirection on maximum principal strain for helmeted head impacts

Abstract

Sporting helmets with linear attenuating strategies are proficient at reducing the risk of traumatic brain injury. However, the continued high incidence of concussion in American football, has led researchers to investigate novel helmet liner strategies. These strategies typically supplement existing technologies by adding or integrating head-helmet decoupling mechanisms. Decoupling strategies aim to redirect or redistribute impact force around the head, reducing impact energy transferred to the brain. This results in decreased brain tissue strain, which is beneficial in injury risk reduction due to the link between tissue strain and concussive injury.

The purpose of this study was to mathematically demonstrate the effect of ten cases, representing theoretical redirection and redistribution helmet liner strategies, on brain tissue strain resulting from impacts to the head. The kinematic response data from twenty head impacts collected in the laboratory was mathematically modified to represent the altered response of the ten different cases and used as input parameters to determine the effect on maximum principal strain (MPS) values, calculated using finite element modeling. The results showed that a reduced dominant coordinate component (contributes the greatest to resultant) of rotational acceleration decreased maximum principal strain in American football helmets. The study theoretically demonstrates that liner strategies, if applied correctly, can influence brain motion, reduce brain tissue strain, and could decrease injury risk in an American football helmet.     

Improving the local solution accuracy of large-scale digital image-based finite element analyses

Digital image-based finite element modeling (DIBFEM) has become a widely utilized approach for efficiently meshing complex biological structures such as trabecular bone. While DIBFEM can provide accurate predictions of apparent mechanical properties, its application to simulate local phenomena such as tissue failure or adaptation has been limited by high local solution errors at digital model boundaries. Furthermore, refinement of digital meshes does not necessarily reduce local maximum errors. The purpose of this study was to evaluate the potential to reduce local mean and maximum solution errors in digital meshes using a post-processing filtration method. The effectiveness of a three-dimensional, boundary-specific filtering algorithm was found to be mesh size dependent. Mean absolute and maximum errors were reduced for meshes with more than five elements through the diameter of a cantilever beam considered representative of a single trabecula. Furthermore, mesh refinement consistently decreased errors for filtered solutions but not necessarily for non-filtered solutions. Models with more than five elements through the beam diameter yielded absolute mean errors of less than 15% for both Von Mises stress and maximum principal strain. When applied to a high-resolution model of trabecular bone microstructure, boundary filtering produced a more continuous solution distribution and reduced the predicted maximum stress by 30%. Boundary-specific filtering provides a simple means of improving local solution accuracy while retaining the model generation and numerical storage efficiency of the DIBFEM technique.     

Finite Element Analysis of Minimal Invasive Transforaminal Lumbar Interbody Fusion

The purpose of our study is to develop and validate three-dimensional finite element models of transforaminal lumbar interbody fusion, and explore the most appropriate method of fixation and fusion by comparing biomechanical characteristics of different fixation method. We developed four fusion models: bilateral pedicle screws fixation with a single cage insertion model (A), bilateral pedicle screws fixation with two cages insertion model (B), unilateral pedicle screws fixation with a single cage insertion model (C), and unilateral pedicle screws fixation with two cages insertion model (D); the models were subjected to different forces including anterior bending, posterior extension, left bending, right bending, rotation, and axial compressive. The von Mises stress of the fusion segments on the pedicle screw and cages was recorded. Angular variation and stress of pedicle screw and cage were compared. There were differences of Von Mises peak stress among four models, but were within the range of maximum force. The angular variation in A, B, C, and D decreased significantly compared with normal. There was no significant difference of angular variation between A and B, and C and D. Bilateral pedicle screws fixation had more superior biomechanics than unilateral pedicle screws fixation. In conclusion, the lumbar interbody fusion models were established using varying fixation methods, and the results verified that unilateral pedicle screws fixation with a single cage could meet the stability demand in minimal invasive transforaminal interbody fusion.     

Deformation of the human brain induced by mild angular head acceleration

Deformation of the human brain was measured in tagged magnetic resonance images (MRI) obtained dynamically during angular acceleration of the head. This study was undertaken to provide quantitative experimental data to illuminate the mechanics of traumatic brain injury (TBI). Mild angular acceleration was imparted to the skull of a human volunteer inside an MR scanner, using a custom MR-compatible device to constrain motion. A grid of MR "tag" lines was applied to the MR images via spatial modulation of magnetization (SPAMM) in a fast gradient echo imaging sequence. Images of the moving brain were obtained dynamically by synchronizing the imaging process with the motion of the head. Deformation of the brain was characterized quantitatively via Lagrangian strain. Consistent patterns of radial-circumferential shear strain occur in the brain, similar to those observed in models of a viscoelastic gel cylinder subjected to angular acceleration. Strain fields in the brain, however, are clearly mediated by the effects of heterogeneity, divisions between regions of the brain (such as the central fissure and central sulcus) and the brain's tethering and suspension system, including the dura mater, falx cerebri, and tentorium membranes.     

Anisotropic finite element models for brain injury prediction: the sensitivity of axonal strain to white matter tract inter-subject variability

Computational models incorporating anisotropic features of brain tissue have become a valuable tool for studying the occurrence of traumatic brain injury. The tissue deformation in the direction of white matter tracts (axonal strain) was repeatedly shown to be an appropriate mechanical parameter to predict injury. However, when assessing the reliability of axonal strain to predict injury in a population, it is important to consider the predictor sensitivity to the biological inter-subject variability of the human brain. The present study investigated the axonal strain response of 485 white matter subject-specific anisotropic finite element models of the head subjected to the same loading conditions. It was observed that the biological variability affected the orientation of the preferential directions (coefficient of variation of 39.41% for the elevation angle—coefficient of variation of 29.31% for the azimuth angle) and the determination of the mechanical fiber alignment parameter in the model (gray matter volume 55.55–70.75%). The magnitude of the maximum axonal strain showed coefficients of variation of 11.91%. On the contrary, the localization of the maximum axonal strain was consistent: the peak of strain was typically located in a 2 cm³ volume of the brain. For a sport concussive event, the predictor was capable of discerning between non-injurious and concussed populations in several areas of the brain. It was concluded that, despite its sensitivity to biological variability, axonal strain is an appropriate mechanical parameter to predict traumatic brain injury.     

Molecular dynamics simulation of crack growth in pure titanium under uniaxial tension

The analysis of crack growth in titanium was performed using molecular dynamics simulation with Embedded Atom Method potentials. The effect of temperature and strain rate on the mechanism of crack growth and the change of microstructure were discussed. After setting an initial crack, the specimen was subjected to uniaxial tension strain up to the total strain level of 0.2 with a constant strain rate. During the period, the shape and the microstructure of crack tip as well as the stress–strain curves were monitored. In the simulation, the gather of voids and stress concentration leading to the crack growth occurred, which are in agreement with experimental results observed by transmission electron microscopy. The transformation from HCP to BCC also occurred at crack tip. The remarkable effect of temperature and strain rate on the growth direction and rate of stacking fault of crack tip was observed. Moreover, initial crack greatly lowered the tension yield point of pure titanium. In the stage of deformation, simulation results showed that loading strain rate and temperature strongly influenced peak stress point, which was increased by the low temperature and high strain, whereas the initial slope of the stress strain curve was independent of loading strain rate.     

Changes in power curve shapes as an indicator of fatigue during dynamic contractions

The purpose of this study was to analyze exercise-induced leg fatigue during a dynamic fatiguing task by examining the shapes of power vs. time curves through the combined use of several statistical methods: B-spline smoothing, functional principal components and (supervised and unsupervised) classification. In addition, granulometric size distributions were also computed to allow for comparison of curves coming from different subjects. Twelve physically active men participated in one acute heavy-resistance exercise protocol which consisted of five sets of 10 repetition maximum leg press with 120 s of rest between sets. To obtain a smooth and accurate representation of the data, a basis of 180 B-splines was used. Functional principal component (FPC) analysis was used to find the dominant modes of variation in the curves. A multivariate cluster over the FPC scores and a k-nearest neighbor classification led to three interpretable groups corresponding to different levels of fatigue. Fatigue-induced changes in the shapes of the power curves were evident, in which curves progressively flatten and develop a second power peak. In a practical setting FPC analysis greatly reduces dimensionality and the use of granulometries allows for comparison of the curve shapes without distorting the time scale.In contrast to the present methodology, which considers each curve as a datum, classical statistical approaches using summary parameters of time series may lead to limited information about the impact of dynamic fatiguing protocols on kinematic and kinetic time-course changes in curve shapes.