Computer Methods in Biomechanics and Biomedical Engineering
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Finite element modeling of human brain response to football helmet impacts T. Darling, J. Muthuswamy & S.D. Rajan To cite this article: T. Darling, J. Muthuswamy & S.D. Rajan (2016): Finite element modeling of human brain response to football helmet impacts, Computer Methods in Biomechanics and Biomedical Engineering, DOI: 10.1080/10255842.2016.1149574 To link to this article: http://dx.doi.org/10.1080/10255842.2016.1149574
Published online: 11 Feb 2016.
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Computer Methods in Biomechanics and Biomedical Engineering, 2016 http://dx.doi.org/10.1080/10255842.2016.1149574
Finite element modeling of human brain response to football helmet impacts T. Darlinga, J. Muthuswamyb and S.D. Rajanc a
School of Engineering Matter, Transport and Energy, Arizona State University, Tempe, AZ, USA; bSchool of Biological and Health Systems Engineering, Arizona State University, Tempe, AZ, USA; cSchool of Sustainable Engineering and the Built Environment, Arizona State University, Tempe, AZ, USA
ARTICLE HISTORY
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ABSTRACT
The football helmet is used to help mitigate the occurrence of impact-related traumatic (TBI) and minor traumatic brain injuries (mTBI) in the game of American football. While the current helmet design methodology may be adequate for reducing linear acceleration of the head and minimizing TBI, it however has had less effect in minimizing mTBI. The objectives of this study are (a) to develop and validate a coupled finite element (FE) model of a football helmet and the human body, and (b) to assess responses of different regions of the brain to two different impact conditions – frontal oblique and crown impact conditions. The FE helmet model was validated using experimental results of drop tests. Subsequently, the integrated helmet–human body FE model was used to assess the responses of different regions of the brain to impact loads. Strain-rate, strain, and stress measures in the corpus callosum, midbrain, and brain stem were assessed. Results show that maximum strain-rates of 27 and 19 s−1 are observed in the brain-stem and mid-brain, respectively. This could potentially lead to axonal injuries and neuronal cell death during crown impact conditions. The developed experimental-numerical framework can be used in the study of other helmet-related impact conditions.
1. Introduction From 1869 to 1905, 18 deaths and 150 serious brain injuries were attributed to the sport of American football (Roper 1927). In response to these troubling results, the first helmet was created in 1893. Initially, the efficacy of a typical helmet was low but as the understanding of the biomechanics involved and the nature of the loading conditions in the sport became better known, the helmet design advanced to almost completely eliminate catastrophic injuries (Hoshizaki & Brien 2004). However, while helmets have had great success in reducing traumatic brain injury (TBI), a same level of reduction was not observed when considering concussion and other minor traumatic brain injuries (mTBI). While this is perhaps due to many factors, the most important one is that reduction in linear acceleration of the head leading to reduced TBI did not minimize other head injuries considered as mTBI. This research is designed to analyze a validated football helmet–human body finite element model in an attempt to better understand how the functional design properties of the helmet affect brain response during two distinct impact conditions.
CONTACT S.D. Rajan
[email protected]
© 2016 Canadian Journal of Philosophy
Received 10 May 2015 Accepted 29 January 2016 KEYWORDS
Football helmet; finite element analysis; mTBI; brain injury; concussion; sports injury; brain tissue
To understand the mechanical properties of the helmet that affect the brain response during impact, the ability to computationally predict human head response, the helmet response, and human head–helmet system response during impact is necessary. The computational tool of choice for a study of this nature is the finite element method. Finding the in vivo material properties for the brain during injury inducing loading conditions is very difficult. To circumvent this problem, cadaveric studies (Hodgson et al. 1970; Nahum et al. 1977; Trosseille et al. 1992; Yoganandan et al. 1995; Hardy & Mason 2007) and animal studies (Miller et al. 2000; Gefen et al. 2003; Prevost et al. 2011; Rashid et al. 2013) are used to define material properties of the brain. While not ideal, these experiments are good approximations and give insight into what should be expected as in vivo material properties. Computing and validating the response of the helmet with or without headforms is comparatively more straightforward. Studies have been carried out to show how the mechanical properties and design of helmets affect stress-distribution, energy attenuation, and accelerations of headforms wearing helmets (Moss & King
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2011; Forero Rueda & Gilchrist 2012; Tinard & Deck 2012). The research shows that in general, for head protection, a hard outer shell with an energy attenuating inside liner works best for minimizing the linear acceleration of the headform. The shell is typically a polycarbonate or composite, and the type of energy attenuating liner is typically a foam such as expanded polystyrene (EPS), expanded polypropylene (EPP), expanded polyethylene (EPE), vinyl nitrile, or cross-linked polyethelene. Since the game of football involves repeated impacts, the foams are restricted to EPP, EPE, vinyl nitrile, and cross-linked EPE (Deck & Willinger 2006). EPS is not suitable because it is characterized as a closed cell foam and undergoes cell rupture during impact. From 2005 to 2010, a study monitoring 1833 collegiate football players was done to determine if the type of football helmet affects the risk of concussion during play (Rowson et al. 2014). The study compared two different helmet designs totaling 1281,444 on-field head impacts from which 64 concussions were diagnosed. The end result showed that one design type reduced the probability of concussion thereby validating the notion that there is connection between helmet design and mTBI. In an earlier paper (Rowson & Duma 2013) introduced a new injury metric, the combined probability of concussion, and showed that it is a valuable method to assess concussion risk in a laboratory setting for evaluating product safety. In an earlier computational study (Post, Oeur, Walsh, et al. 2013) using the University College Dublin Brain Trauma Model (UCDBTM) finite element model for the human head, response of three different football helmet designs were studied. The researchers constructed an impact simulating experiment and using each helmet, determined an acceleration profile to apply to the human head model. Each helmet type resulted in different acceleration profiles. However because they did not use a numerical model of the helmet in the study, only broad statements regarding brain response to impact loads could be made (Post, Oeur, et al. 2013). Similarly, a study by Deck and Willinger (2006) proved that optimization against headform response and optimization against human head response do not lead to the same results. Helmet studies have also been carried out in areas not related to sports such as transportation and military helmet applications to assess how the helmet properties affected the brain response when the helmet and head are coupled in one finite element model. Pinnoji and Mahajan (2007) compared two models – frontal impact on a head and generic helmet model using an EPS foam liner and a polycarbonate shell, and a model with no helmet. The study showed that the coup pressures in the head were substantially reduced by using the helmet. However the study did not identify specific anatomical structures in
the brain and neglected the rotational contributions by excluding the neck anatomy in the model. More recently, Salimi Jazi et al. (2014) studied the influence of helmet padding materials on the human brain under ballistic impact. They modeled the human head–neck system with the helmet and determined the sensitivity of pad stiffness to resultant brain pressures. However, the model was not validated in this study. Tinard and Deck (2012), using the Strasbourg University Finite Element Head Model and a motorcycle helmet model coupled the helmet– head system and compared the results for risk of injury during motorcycle crash impacts. The helmet was validated against experimental data and the study provides insight into how to couple the human head and helmet. It was determined that for current motorcycle standard test conditions, the head is still susceptible to brain injury based on the determined brain response. Furthermore, the study found that if the neck is ignored in a simulation, the proper angular accelerations experienced by the head during impact cannot be found and as a result, the brain response will be incorrectly predicted. In the present study, a state-of-the-art finite element model of the human body, i.e. the Global Human Body Model Consortium (GHBMC) full body model, is coupled with a fully validated finite element model of a football helmet. The LS-DYNA finite element model of the human head and its different anatomical regions developed at Wayne State University and Wake University was used in this study (Chatelin et al. 2010; Bilston 2011; Mao et al. 2013). The full body model is used so that all the relevant anatomical features are included in studying the brain response to head–helmet impact scenarios. The results will help isolate how the design features of the football helmet interact and contribute to the response of brain material. The research methods are presented in Section 2. The commercially available program LS-DYNA v971 (LSTC 2015) is used in this study. The numerical and experimental validation of the helmet finite element model using publicly available data as well as experiments conducted in our laboratory are discussed. The results from the execution of the finite element models are presented in Section 3. In Section 4, we discuss the results from the coupled helmet–human body models and injury thresholds, and these are followed by concluding remarks.
2. Methods 2.1. Helmet model description In this study the football helmet model is created containing three components: the shell, the energy absorbing liner, and the comfort liner. The face mask and retention system were not included because they are not required
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Figure 1. Finite element model of the helmet headform and impactor system (a) section cut of the helmet headform system (b) planar cross section of the helmet headform system showing critical points for measurements. Table 1. Model material properties. Component Energy foam Comfort foam Outer shell Headform Impactor
Material High density foam Low density foam Polycarbonate Magnesium alloy 6061 Aluminum alloy
Density (kg/mm3) 2.8 × 10−7 3.0 × 10−8 1.1996 × 10−6 1.74 × 10−6 2.7 × 10−6
Young’s modulus (MPa) 0.08 0.0448 2415 45,000 206,000
Poisson’s ratio 0 0 0.329 0.3 0.3
Table 2. Finite element model details. Component Energy foam Comfort foam Outer shell Headform Impactor
Material MAT_LOW_DENSITY_FOAM MAT_LOW_DENSITY_FOAM MAT_ELASTIC MAT_ELASTIC MAT_ELASTIC
Element type 8-Noded Hexahedral 8-Noded Hexahedral 4-Noded Quadrilateral thin shell 4-Noded Quadrilateral thin shell 8-Noded Hexahedral
in the National Operating Committee on Standards for Athletic Equipment (NOCSAE) standardized testing standards for helmets. Figure 1(a) shows the helmet with a cutout in the model to show the cross section of the helmet features and the headform surface. As discussed later in Section 2.3, the headform is used in the experiments that help validate the helmet model. Geometry: As a geometry reference and tool for model validation of the helmet, this study used the Riddell Attack Revolution Youth helmet (L) (Riddell 2014). The headform geometry was created by using the top half of the headform specified in NOCSAE standard (DOC(ND) 002 – 13). The entire geometry was created in SolidworksTM (SolidWorks 2014). Reference points were measured on the helmet and images of the helmet were mapped to those reference points for use in SolidworksTM. This approach resulted in a geometry that was a reasonable approximation to the exact surface and provided a parameterized model for possible helmet design optimization. The
Formulation 1-integration point 1-integration point 5-integration point through thickness Full-integration 1-integration point
finite element mesh was created using Hypermesh (Altair 2011) and careful attention was paid to the mesh quality as deformations in various parts of the model can be large leading to numerical instabilities and contact algorithm difficulties. Since material properties for the various components of the helmet were not readily available, initial material properties were acquired through literature review (efunda 2014). The material properties were then tuned to match the experimental results for the energy absorbing foam. The final material property values are listed in Table 1. The impactor (114 mm × 43 mm × 381 mm) has a total mass of 5.0 kg. The Shell: The outer shell was determined to be polycarbonate-unfilled-low-viscosity material (Zhang 2001) and was meshed using 4-noded thick shell elements with the full-integration element formulation (Type 16) and 5 integration points through the thickness. To model its behavior, a linear elastic material model within LS-DYNA
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Table 3. Response values for various mesh densities.
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Mesh density Coarse Medium Fine
Impactor max. velocity (mm/ms) 1.83 1.95 2.01
Impactor max. acceleration (mm/ms2) 0.66 0.74 0.79
was used. No plastic deformation in the shell was assumed because the loading conditions were designed to be below levels that induced damage to the helmet. To ensure this assumption was valid, the maximum strain and the principal stresses in the shell were monitored and for all simulations, these values stayed below the 10% elongation at yield and 60 MPa tensile strength, known elastic limits for the material. While strain rate dependency may exist, no strain rate dependence was used due to lack of publicly available data and for the sake of retaining the simplicity of analysis. The Liners: The helmet liners were modeled as opencelled foam (OCF) (McIntosh & McCrory 2000). As a result, quasi-static compressive experiments could be performed and the resulting stress–strain curves could be input directly into LS-DYNA to define the material behavior. The LS-DYNA keyword MAT_LOW_ DENSITY_FOAM implements the constitutive model for this material. In tension, this material model assumes a linear elastic behavior until a particular defined tearing point. It should be noted that some of these foams are also highly strain rate dependent. However in the absence of experimental data, only one strain rate data was used. The comfort and energy absorbing liners were identified as a type of OCF and publicly available uniaxial compression tests results were used. The stress–strain curves were input directly into LS-DYNA. The foams were meshed using 8-noded hexahedral elements using 1-point integration (element formulation 1) in order to have a manageable number of elements, better control over the mesh quality, and prevent negative volumes in the elements due to the large deformations experienced in the analysis. The Headform: The headform shell was considered rigid because it was an approximation for the solid headform. The finite elements used were rigid 4-noded thin shell elements (Type 16) with one integration point through the thickness. The material for the headform is defined in the NOCSAE standard DOC (ND) 002 – 13 (NOCSAE 2013) where magnesium alloys are recommended because of their light weight and strength. The material model for this component was MAT_ELASTIC. For simplicity of the model, numerical stability, and better control of the contact initiated between the headform and soft foam, 4-noded thin quadrilateral elements were used. To define the interaction between the components, contact details are used in the finite element model. The comfort foam and energy foam as well as the outer shell
Shell foam max. acceleration (mm/ms2) 4.43 5.76 6.89
and the energy foam are coupled via tied contact. When defining automatic contact between two dissimilar materials such as the comfort foam and the magnesium headform, care had to be taken to see how the penalty function is implemented in contact. In our LS-DYNA model, the SOFT = 1 command is implemented which causes the contact stiffness to be determined based on stability considerations, taking into account the time step and nodal masses. Table 2 summarizes some of the details of the finite element model. 2.2. Helmet model numerical validation To ensure accuracy of the finite element results, a quality control step was implemented that included convergence analysis (Roache 1998) and monitoring some important energy-related parameters that are an integral part of a typical explicit finite element analysis (Bansal et al. 2009; Stahlecker et al. 2009; Deivanayagam et al. 2013). For example, the energy ratios are required to be between 0.9 and 1.1, the maximum hourglass energy ratio is expected to be below 0.1 etc. for the model results to be acceptable. Three simulations with varying mesh densities were completed to carry out the convergence analysis and select a model that would be used for the subsequent finite element analyses. The coarse mesh had 45,339 elements, the medium mesh had 84,008 elements, and the fine mesh had 205,402 elements. The response of the impactor and the helmet shell and hard foam were monitored (Figure 1(b)). For the impactor, the maximum acceleration of the center of gravity (CG) and the velocity of a corner node of the impactor were selected. For the helmet, acceleration of the nodes at the front edge of the helmet was used. The results are summarized in Table 3. The energy checks were all satisfied confirming that the finite element analysis performed with reasonable and acceptable accuracy. The energy ratio was between 0.9 and 1.1 for the simulations. The sliding energy ratio and hourglass energy ratio was 0.04 and 0.02, respectively. The kinetic energy ratio and internal energy ratio 0.99 and 0.92, respectively. 2.3. Helmet model experimental validation To compare the numerical model of the headform with experimental results, a drop test impacting the crown of the helmet was performed. The experimental setup
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The low frequency response shows that the model was able to recreate the salient features of the experimental acceleration profiles. The maximum acceleration for the simulation was 68.1 g and the average maximum acceleration for the experiments was 67.3 g with a standard deviation of 2.2 g. The maximum acceleration in the simulation occurred at 0.0131 s and the experiments averaged to 0.0139 s.
Figure 2. Drop test setup showing helmet mounted on Al-6061 headform and an ABS plastic cap. Y-Acceleration (Raw Data) vs Time Model Validation
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2.4. Human body model and injury thresholds
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Figure 3. Experimental validation of Y acceleration in impactor.
was designed to be a reasonable approximation to the NOCSAE standard drop test system. The system is shown in Figure 2. In the test, a 5.95 kg block at 458.7 mm above the impact site was dropped to obtain an impact velocity of 3 m/s. An accelerometer was placed on the top of the impact plate to record the response of the system. The vertical (Y) acceleration of the impactor as obtained from the experiments was compared with the finite element model simulation as shown in Figures 3 (before filtering) and 4 (after filtering). The frequency content of the signal was determined by a fast Fourier t ransform (FFT) of the experimental signal. The FFT shows that the majority of the signal amplitude comes from the low frequency response.
The GHBMC full body model is a detailed finite element model (Chatelin et al. 2010; Bilston 2011; Mao et al. 2013). Supine magnetic resonance imaging and CT scans of an average adult male head were used to gather the skin surface, skull and facial bones, sinuses, cerebrum, cerebellum, lateral ventricles, corpus callosum, thalamus, brainstem, and cerebral white matter. Where anatomical features could not be defined with the imaging techniques, literature reviews were used to create the features – for example, differentiating the skull with outer cortical layer, middle cancellous layer, and inner cortical layer. The model has a total of 270,552 elements including 150,074 hexahedral elements, 352 pentahedral, 60,828 tetrahedral, 45,140 quadrilateral shell, 14,136 triangular shell, and 22 onedimensional beam elements. Brain tissue is a hydrated soft tissue that consists of 78% water that displays both elastic and viscous properties. As a result, the material properties of the head were determined by a large set of mechanical tests that have been performed on cadaver or animal specimens using compression, tension, shear, indentation, or magnetic resonance electrography methods. In summary, the gray matter and white matter were defined as linear viscoelastic materials with the white matter 25% stiffer than the gray. The cortical and cancellous bones were modeled with elastic-plastic materials, and the flesh was defined as viscoelastic material, which provides the best simulation robustness. The skin membranes, falx, tentorium, dura, arachnoid, and pia were defined as elastic materials.
3. Results With the combined finite element model (helmet plus GHBMC body model), it is now possible to compute the brain response in specific anatomical structures particularly relevant to mTBI. McAllister et al. (2011) showed that the maximum strain and strain rate fields in brain tissue during impact correlate with the changes in white matter integrity in the area of the corpus callosum. Therefore, the brain response data for the current study focuses on stress, strain and strain rate in the midbrain, corpus callosum, and the brain stem. Two load conditions were tested with
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50 40 30 20 10 0 -10
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Figure 4. Filtered experimental and simulation data for low frequency response (Y acceleration in impactor).
the helmet–human system – a frontal impact, defined by an impact angle of 30° with respect to the horizontal plane (Figure 6) and a crown impact (Figure 7) with the impactor velocity of 3 m/s. The loading conditions were not intended to replicate impacts that cause mTBI but were designed to replicate impacts that the NOCSAE standard deemed as dangerous impact conditions. We first investigate the extent of the deformations (resultant displacement) in the model as the impactcreated wave travels through the body. The finite element analyses were executed for a total time of 15 ms for crown
impact and for 30 ms for the oblique frontal impact. These time values were determined via trial-and-error to be adequate since the maximum response (principal stresses and strain, and stress and strain rates) occurs before that time value. Figure 5 shows the (final) state of the body at 15 ms and shows the time at which each identified node exceeded a deformation value of 0.25 mm, a value that is significantly smaller than the maximum absolute displacement of approximately 300 mm that is seen in the FE simulation. Figures 6 and 7 show the corpus callosum, midbrain, and brainstem highlighted in yellow, blue and green respectively inside the skull (not to be confused with parts of the helmet that are colored yellow and green) as they deform relative to the surrounding anatomical structures during the oblique frontal impact and crown impact, respectively. The relative resultant displacement versus time plots for corpus callosum, midbrain, and brainstem are shown in Figures 8 and 9, relative to the center of gravity (CG) of the skull. A positive displacement is when the item in question is moving faster than the CG. A qualitative assessment of the coup pressures can be made in various anatomical parts of the brain by looking at the relative magnitude of this displacement. The maximum principal and shear strains, strain rate, and stress values are shown in Figures 10–15 for the midbrain (MB), corpus callosum (CC) and brainstem (BS). Figures 10 and 11 show that the maximum principal strain due to frontal oblique impact condition is 8.9%
Figure 5. Displacement at time t = 15 ms for the crown impact model. Time values correspond to time when the resultant displacement is greater than 0.25 mm.
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Figure 6. Deformation of the human-helmet system during frontal oblique impact (time in ms).
Figure 7. Deformation of the human-helmet system during crown impact (time in ms).
and for the crown impact is 4.5% with both occurring in the brain-stem. While the strains doubled for the frontal oblique impact condition, they are still lower than the previously defined thresholds for brain injury (Zhang et al. 2004). Figures 12 and 13 show the maximum von Mises stress for the frontal oblique impact is 659 Pa and for the crown impact is 476 Pa with both occurring in the brain-stem. Figures 14 and 15 show that the maximum principal strain rate is 0.016 ms−1 for the front oblique impact and 0.027 ms−1 for the crown impact, both occurring in the brain-stem.
4. Discussions The integration of a full human body model in this study allows for an elimination of assumptions regarding the relationship between the head and the neck, and the neck’s relationship to the rest of the body. Simulation results in Figure 5 indicate that the backbone experiences the greatest deformation and the displacement wave reaches down to about the pelvis area of the full human body model indicating the need for including the torso in the analysis. The crown impact results in oscillatory displacements of brain tissue when subtracted from the rigid motion of the
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Figure 8. Frontal oblique impact displacement of corpus callosum, midbrain, and brainstem components.
Figure 11. Strain during crown impact.
Figure 12. Frontal impact maximum stress values. Figure 9. Crown impact displacement of corpus callosum, midbrain, and brainstem components.
Figure 10. Strain during frontal oblique impact.
Figure 13. Crown impact maximum stress values.
skull. A different phenomenon occurs with frontal oblique loading as shown in Figures 8 and 9. The corpus callosum is pushed toward the top of the skull whereas the midbrain and brainstem components are pulled toward the neck. Several publications mention injury thresholds for stress and strains in the brain due to impacts experienced during a game of football by analyzing concussion-causing impacts with validated finite element models of the brain (Willinger & Baumgartner 2003; Zhang et al. 2004). By analyzing head–head impact occurrences of mTBI with
a finite element model, Zhang predicted injury to occur with 50% probability at 7.8 kPa (von Mises) and principal strain of 0.19. Willinger and Baumgartner (2003) predicted injury at 18 kPa (von Mises) by analyzing brain tissue in car accidents with the finite element method and comparing the results against known injury cases. In-vitro testing performed by Pfister et al. (2003) to create mild to severe axonal injuries showed that axonal injury and neural cell death occur when applying principal strains from 20 to 70% and strain rates in the range of 20–90 s−1.
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Figure 14. Frontal impact maximum strain rate values.
for brain injury (Zhang et al. 2004). Not surprisingly, the maximum von Mises stresses (659 Pa for the frontal oblique and 476 Pa for the crown impact) also occur in the brain-stem region (Figures 12 and 13). However, they are a small fraction of the injury causing values reported by Willinger and Baumgartner (2003) and Zhang et al. (2004). However, the maximum strain rate values observed in the brain-stem in Figures 14 and 15 (16 and 27 s−1 for frontal oblique and crown impact, respectively) when compared against the thresholds for injury defined earlier show that the crown impact generates a potential injury inducing loading condition (Pfister et al. 2003) in the brain-stem and mid-brain. The maximum values of stress, principal strain, and principal strain rate in the brainstem illustrate an agreement with the clinical evaluations seen when studying patients who have experienced an mTBI. The brainstem is associated with regulating consciousness of the patient and so damage due to high strain-rates in that region could cause the patient to lose consciousness, which occurs in some cases for mTBI. Using this current model, the crown impact would be characterized as a potentially damaging loading condition due to the strain rates experienced in the brainstem and mid-brain. The maximum values of principal strain, shear strain, von Mises stress and strain rates are summarized in Tables 4 and 5.
Figure 15. Crown impact maximum strain rate values.
5. Concluding remarks
The maximal principal strains (of 8.9% under frontal oblique and 4.5% under crown impact) are observed in the brain-stem regions under both loading conditions followed closely by the mid-brain region (Figures 10 and 11). While the maximal principal strain doubled for the brainstem under the frontal oblique impact condition, they are still lower than the previously defined thresholds
An integrated human body–football helmet finite element model was created using the GHBMC human body model and analyzed using LS-DYNA. The Riddell Revolution AttackTM helmet was modeled with particular attention paid to its polycarbonate shell and bi-layer foam system. The finite element model was validated by comparing the performance of the model with experimental drop test. The integrated model was then created
Table 4. Maximum response values for crown impact. Max principal strain Max shear strain Strain rate (ms−1) Shear strain rate (ms−1) von Mises (Pa) Tresca (Pa)
Brainstem 0.045 0.044 0.027 0.027 476 274
Midbrain 0.045 0.037 0.019 0.018 345 196
Corpus callosum 0.023 0.021 0.0099 0.0097 131 76
Table 5. Maximum response values for frontal oblique impact. Maximum principal strain Maximum shear strain Strain rate (ms−1) Shear strain rate (ms−1) von Mises stress (Pa) Tresca stress (Pa)
Brainstem 0.088 0.08 0.016 0.017 659 380
Midbrain 0.029 0.028 0.017 0.016 443 253
Corpus callosum 0.076 0.073 0.0098 0.0082 291 166
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by placing the helmet model over the skull portion of the GHBMC model. This model was then subjected to centric and non-centric impacts. A crown impact and a frontal oblique impact were performed and the strainrate, strain, and stress values experienced in the corpus callosum, midbrain, and brain stem were determined. The loading conditions were not intended to replicate impacts that cause mTBI but were designed to replicate impacts that the NOCSAE standard deemed as dangerous impact conditions. According to previously defined injury thresholds, the two loading conditions used in this study result in potential injury conditions through the high strain rates observed in the corpus callosum, midbrain, and brain stem. The coupled human-helmet system provides anatomical structure specific feedback during the occurrence of potential mTBI and helps establish a better understanding of the injury causing mechanisms. Moreover, the developed framework can potentially be used to study other helmet-related impact scenarios.
Acknowledgements The human body model was supplied to Arizona State University through the Global Human Body Modeling Consortium. The version used in this research is v4.1.1.
Disclosure statement No potential conflict of interest was reported by the authors.
Notes on contributors Tim Darling is currently a design engineer working for Honeywell Aerospace in Phoenix, AZ. He graduated from Arizona State University with a Master of Science degree in mechanical engineering. Jit Muthuswamy is an associate professor in the School of Biological and Health Systems Engineering at ASU. His research interests are in the areas of microelectromechanical systems (MEMS) for neural communication and plasticity in the central nervous system. His primary efforts are directed towards understanding and treating brain dysfunction. One of his main research thrusts is in the development of multi-functional neural prosthesis using MEMS technologies for precise tracking, communication, stimulation and control of neuronal function and dysfunction. Using these novel technologies in models of brain injury, he is interested in understanding the neurochemical and neuroelectrical dynamics that determine neurological outcome and the neuroprotective role of specific genes. Subramaniam Rajan is a professor of civil, mechanical and aerospace engineering in the School of Sustainable Engineering and the Built Environment. His research interests include development of constitutive models for composite materials, experimental techniques for the determination of material properties of composite materials, finite element analysis,
design optimization, and high-performance parallel computations. Using these tools, his research focus is on developing ballistic and blast mitigation solutions. He is the author of an undergraduate textbook on structural analysis and design, and a graduate book on object-oriented numerical analysis.
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Moss WC, King MJ. 2011. Impact response of US Army and National Football League helmet pad systems. Livermore, CA: Lawrence Livermore National Laboratory. Nahum AM, Smith R, Ward CC. 1977. Intracranial pressure dynamics during head impact. Proceedings of 21st Stapp car crash conference, SAE Paper No. 770922; New Orleans, LA. NOCSAE. 2013. Standard performance specification for newly manufactured football helmets. DOC (ND) 002 – 13; Overland Park, KS: National Operating Committee on Standards for Athletic Equipment. Pfister BJ, Weihs TP, Betenbaugh M, Bao G. 2003. An in vitro uniaxial stretch model for axonal injury. Ann Biomed Eng. 31:589–598. Pinnoji PK, Mahajan P. 2007. Finite element modelling of helmeted head impact under frontal loading. Sadhana. 32:445–458. Post A, Oeur A, Hoshizaki B, Gilchrist MD. 2013. An examination of American football helmets using brain deformation metrics associated with concussion. Mater Des. 45:653–662. Post A, Oeur A, Walsh E, Hoshizaki B, Gilchrist MD. 2013. A centric/non-centric impact protocol and finite element model methodology for the evaluation of American football helmets to evaluate risk of concussion. Comput Methods Biomech Biomed Eng. 17:1785–1800. Prevost TP, Balakrishnan A, Suresh S, Socrate S. 2011. Biomechanics of brain tissue. Acta Biomater. 7:83–95. Rashid B, Destrade M, Gilchrist MD. 2013. Mechanical characterization of brain tissue in simple shear at dynamic strain rates. J Mech Behav Biomed Mater. 28:71–85. Riddell. 2014. Available from: http://team.riddell.com/shopriddell/helmet/revolution-attack-i-youth-helmet/ Roache PJ. 1998. Verification and validation in computational science and engineering. Albuquerque, NM: Hermosa Publishers. Roper WW. 1927. Football today and tomorrow. New York, NY, Duffield and Co.; p. 155–156.
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Rowson S, Duma SM. 2013. Brain injury prediction: Assessing the combined probability of concussion using linear and rotational head acceleration. Ann Biomed Eng. 41:873–882. Rowson S, Duma SM, Greenwald RM, Beckwith JG, Chu JJ, Guskiewicz KM, Mihalik JP, Crisco JJ, Wilcox BJ, McAllister TW, et al. 2014. Can helmet design reduce the risk of concussion in football? J Neurosurg. 120:919–922. Salimi Jazi M, Rezaei A, Karami G, Azarmi F, Ziejewski M. 2014. A computational study of influence of helmet padding materials on the human brain under ballistic impacts. Comput Methods Biomech Biomed Eng. 17:1368–1382. SolidWorks Education Edition. 2014. Dessault Systémes. Copyright© 1997–2012. Stahlecker Z, Mobasher B, Rajan SD, Pereira JM. 2009. Development of reliable modeling methodologies for engine fan blade out containment analysis. Part II: finite element analysis. Int J Impact Eng. 36:447–459. Tinard V, Deck C. 2012. New methodology for improvement of helmet performances during impacts with regards to biomechanical criteria. Mater Des. 37:79–88. Trosseille X, Tarriere C, Lavaste F, Guilon F, Domont A. 1992. Development of a F.E.M. of the human head according to a specific test protocol. Proceedings of 36th Stapp Car Crash Conference, SAE Paper No. 922527; Seattle, WA. Willinger R, Baumgartner D. 2003. Numerical and physical modelling of the human head under impact – towards new injury criteria. Int J Veh Des. 32:94–115. Yoganandan N, Pintar F, Sances A, Walsh P, Ewing C, Thomas D, Snyder R. 1995. Biomechanics of skull fracture. J Neurotrauma. 12:659–668. Zhang L, Yang KH, King AI. 2004. A proposed injury threshold for mild traumatic brain injury. Trans ASME. 126:226–236. Zhang LY. 2001. Computational biomechanics of traumatic brain injury: an investigation of head impact response and American football head injury [Ph.D dissertation]. Detroit, MI: Wayne State University.
ISSN: 1025-5842 (Print) 1476-8259 (Online) Journal homepage: http://www.tandfonline.com/loi/gcmb20
Finite element modeling of human brain response to football helmet impacts T. Darling, J. Muthuswamy & S.D. Rajan To cite this article: T. Darling, J. Muthuswamy & S.D. Rajan (2016): Finite element modeling of human brain response to football helmet impacts, Computer Methods in Biomechanics and Biomedical Engineering, DOI: 10.1080/10255842.2016.1149574 To link to this article: http://dx.doi.org/10.1080/10255842.2016.1149574
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Computer Methods in Biomechanics and Biomedical Engineering, 2016 http://dx.doi.org/10.1080/10255842.2016.1149574
Finite element modeling of human brain response to football helmet impacts T. Darlinga, J. Muthuswamyb and S.D. Rajanc a
School of Engineering Matter, Transport and Energy, Arizona State University, Tempe, AZ, USA; bSchool of Biological and Health Systems Engineering, Arizona State University, Tempe, AZ, USA; cSchool of Sustainable Engineering and the Built Environment, Arizona State University, Tempe, AZ, USA
ARTICLE HISTORY
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ABSTRACT
The football helmet is used to help mitigate the occurrence of impact-related traumatic (TBI) and minor traumatic brain injuries (mTBI) in the game of American football. While the current helmet design methodology may be adequate for reducing linear acceleration of the head and minimizing TBI, it however has had less effect in minimizing mTBI. The objectives of this study are (a) to develop and validate a coupled finite element (FE) model of a football helmet and the human body, and (b) to assess responses of different regions of the brain to two different impact conditions – frontal oblique and crown impact conditions. The FE helmet model was validated using experimental results of drop tests. Subsequently, the integrated helmet–human body FE model was used to assess the responses of different regions of the brain to impact loads. Strain-rate, strain, and stress measures in the corpus callosum, midbrain, and brain stem were assessed. Results show that maximum strain-rates of 27 and 19 s−1 are observed in the brain-stem and mid-brain, respectively. This could potentially lead to axonal injuries and neuronal cell death during crown impact conditions. The developed experimental-numerical framework can be used in the study of other helmet-related impact conditions.
1. Introduction From 1869 to 1905, 18 deaths and 150 serious brain injuries were attributed to the sport of American football (Roper 1927). In response to these troubling results, the first helmet was created in 1893. Initially, the efficacy of a typical helmet was low but as the understanding of the biomechanics involved and the nature of the loading conditions in the sport became better known, the helmet design advanced to almost completely eliminate catastrophic injuries (Hoshizaki & Brien 2004). However, while helmets have had great success in reducing traumatic brain injury (TBI), a same level of reduction was not observed when considering concussion and other minor traumatic brain injuries (mTBI). While this is perhaps due to many factors, the most important one is that reduction in linear acceleration of the head leading to reduced TBI did not minimize other head injuries considered as mTBI. This research is designed to analyze a validated football helmet–human body finite element model in an attempt to better understand how the functional design properties of the helmet affect brain response during two distinct impact conditions.
CONTACT S.D. Rajan
[email protected]
© 2016 Canadian Journal of Philosophy
Received 10 May 2015 Accepted 29 January 2016 KEYWORDS
Football helmet; finite element analysis; mTBI; brain injury; concussion; sports injury; brain tissue
To understand the mechanical properties of the helmet that affect the brain response during impact, the ability to computationally predict human head response, the helmet response, and human head–helmet system response during impact is necessary. The computational tool of choice for a study of this nature is the finite element method. Finding the in vivo material properties for the brain during injury inducing loading conditions is very difficult. To circumvent this problem, cadaveric studies (Hodgson et al. 1970; Nahum et al. 1977; Trosseille et al. 1992; Yoganandan et al. 1995; Hardy & Mason 2007) and animal studies (Miller et al. 2000; Gefen et al. 2003; Prevost et al. 2011; Rashid et al. 2013) are used to define material properties of the brain. While not ideal, these experiments are good approximations and give insight into what should be expected as in vivo material properties. Computing and validating the response of the helmet with or without headforms is comparatively more straightforward. Studies have been carried out to show how the mechanical properties and design of helmets affect stress-distribution, energy attenuation, and accelerations of headforms wearing helmets (Moss & King
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2011; Forero Rueda & Gilchrist 2012; Tinard & Deck 2012). The research shows that in general, for head protection, a hard outer shell with an energy attenuating inside liner works best for minimizing the linear acceleration of the headform. The shell is typically a polycarbonate or composite, and the type of energy attenuating liner is typically a foam such as expanded polystyrene (EPS), expanded polypropylene (EPP), expanded polyethylene (EPE), vinyl nitrile, or cross-linked polyethelene. Since the game of football involves repeated impacts, the foams are restricted to EPP, EPE, vinyl nitrile, and cross-linked EPE (Deck & Willinger 2006). EPS is not suitable because it is characterized as a closed cell foam and undergoes cell rupture during impact. From 2005 to 2010, a study monitoring 1833 collegiate football players was done to determine if the type of football helmet affects the risk of concussion during play (Rowson et al. 2014). The study compared two different helmet designs totaling 1281,444 on-field head impacts from which 64 concussions were diagnosed. The end result showed that one design type reduced the probability of concussion thereby validating the notion that there is connection between helmet design and mTBI. In an earlier paper (Rowson & Duma 2013) introduced a new injury metric, the combined probability of concussion, and showed that it is a valuable method to assess concussion risk in a laboratory setting for evaluating product safety. In an earlier computational study (Post, Oeur, Walsh, et al. 2013) using the University College Dublin Brain Trauma Model (UCDBTM) finite element model for the human head, response of three different football helmet designs were studied. The researchers constructed an impact simulating experiment and using each helmet, determined an acceleration profile to apply to the human head model. Each helmet type resulted in different acceleration profiles. However because they did not use a numerical model of the helmet in the study, only broad statements regarding brain response to impact loads could be made (Post, Oeur, et al. 2013). Similarly, a study by Deck and Willinger (2006) proved that optimization against headform response and optimization against human head response do not lead to the same results. Helmet studies have also been carried out in areas not related to sports such as transportation and military helmet applications to assess how the helmet properties affected the brain response when the helmet and head are coupled in one finite element model. Pinnoji and Mahajan (2007) compared two models – frontal impact on a head and generic helmet model using an EPS foam liner and a polycarbonate shell, and a model with no helmet. The study showed that the coup pressures in the head were substantially reduced by using the helmet. However the study did not identify specific anatomical structures in
the brain and neglected the rotational contributions by excluding the neck anatomy in the model. More recently, Salimi Jazi et al. (2014) studied the influence of helmet padding materials on the human brain under ballistic impact. They modeled the human head–neck system with the helmet and determined the sensitivity of pad stiffness to resultant brain pressures. However, the model was not validated in this study. Tinard and Deck (2012), using the Strasbourg University Finite Element Head Model and a motorcycle helmet model coupled the helmet– head system and compared the results for risk of injury during motorcycle crash impacts. The helmet was validated against experimental data and the study provides insight into how to couple the human head and helmet. It was determined that for current motorcycle standard test conditions, the head is still susceptible to brain injury based on the determined brain response. Furthermore, the study found that if the neck is ignored in a simulation, the proper angular accelerations experienced by the head during impact cannot be found and as a result, the brain response will be incorrectly predicted. In the present study, a state-of-the-art finite element model of the human body, i.e. the Global Human Body Model Consortium (GHBMC) full body model, is coupled with a fully validated finite element model of a football helmet. The LS-DYNA finite element model of the human head and its different anatomical regions developed at Wayne State University and Wake University was used in this study (Chatelin et al. 2010; Bilston 2011; Mao et al. 2013). The full body model is used so that all the relevant anatomical features are included in studying the brain response to head–helmet impact scenarios. The results will help isolate how the design features of the football helmet interact and contribute to the response of brain material. The research methods are presented in Section 2. The commercially available program LS-DYNA v971 (LSTC 2015) is used in this study. The numerical and experimental validation of the helmet finite element model using publicly available data as well as experiments conducted in our laboratory are discussed. The results from the execution of the finite element models are presented in Section 3. In Section 4, we discuss the results from the coupled helmet–human body models and injury thresholds, and these are followed by concluding remarks.
2. Methods 2.1. Helmet model description In this study the football helmet model is created containing three components: the shell, the energy absorbing liner, and the comfort liner. The face mask and retention system were not included because they are not required
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Figure 1. Finite element model of the helmet headform and impactor system (a) section cut of the helmet headform system (b) planar cross section of the helmet headform system showing critical points for measurements. Table 1. Model material properties. Component Energy foam Comfort foam Outer shell Headform Impactor
Material High density foam Low density foam Polycarbonate Magnesium alloy 6061 Aluminum alloy
Density (kg/mm3) 2.8 × 10−7 3.0 × 10−8 1.1996 × 10−6 1.74 × 10−6 2.7 × 10−6
Young’s modulus (MPa) 0.08 0.0448 2415 45,000 206,000
Poisson’s ratio 0 0 0.329 0.3 0.3
Table 2. Finite element model details. Component Energy foam Comfort foam Outer shell Headform Impactor
Material MAT_LOW_DENSITY_FOAM MAT_LOW_DENSITY_FOAM MAT_ELASTIC MAT_ELASTIC MAT_ELASTIC
Element type 8-Noded Hexahedral 8-Noded Hexahedral 4-Noded Quadrilateral thin shell 4-Noded Quadrilateral thin shell 8-Noded Hexahedral
in the National Operating Committee on Standards for Athletic Equipment (NOCSAE) standardized testing standards for helmets. Figure 1(a) shows the helmet with a cutout in the model to show the cross section of the helmet features and the headform surface. As discussed later in Section 2.3, the headform is used in the experiments that help validate the helmet model. Geometry: As a geometry reference and tool for model validation of the helmet, this study used the Riddell Attack Revolution Youth helmet (L) (Riddell 2014). The headform geometry was created by using the top half of the headform specified in NOCSAE standard (DOC(ND) 002 – 13). The entire geometry was created in SolidworksTM (SolidWorks 2014). Reference points were measured on the helmet and images of the helmet were mapped to those reference points for use in SolidworksTM. This approach resulted in a geometry that was a reasonable approximation to the exact surface and provided a parameterized model for possible helmet design optimization. The
Formulation 1-integration point 1-integration point 5-integration point through thickness Full-integration 1-integration point
finite element mesh was created using Hypermesh (Altair 2011) and careful attention was paid to the mesh quality as deformations in various parts of the model can be large leading to numerical instabilities and contact algorithm difficulties. Since material properties for the various components of the helmet were not readily available, initial material properties were acquired through literature review (efunda 2014). The material properties were then tuned to match the experimental results for the energy absorbing foam. The final material property values are listed in Table 1. The impactor (114 mm × 43 mm × 381 mm) has a total mass of 5.0 kg. The Shell: The outer shell was determined to be polycarbonate-unfilled-low-viscosity material (Zhang 2001) and was meshed using 4-noded thick shell elements with the full-integration element formulation (Type 16) and 5 integration points through the thickness. To model its behavior, a linear elastic material model within LS-DYNA
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Table 3. Response values for various mesh densities.
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Mesh density Coarse Medium Fine
Impactor max. velocity (mm/ms) 1.83 1.95 2.01
Impactor max. acceleration (mm/ms2) 0.66 0.74 0.79
was used. No plastic deformation in the shell was assumed because the loading conditions were designed to be below levels that induced damage to the helmet. To ensure this assumption was valid, the maximum strain and the principal stresses in the shell were monitored and for all simulations, these values stayed below the 10% elongation at yield and 60 MPa tensile strength, known elastic limits for the material. While strain rate dependency may exist, no strain rate dependence was used due to lack of publicly available data and for the sake of retaining the simplicity of analysis. The Liners: The helmet liners were modeled as opencelled foam (OCF) (McIntosh & McCrory 2000). As a result, quasi-static compressive experiments could be performed and the resulting stress–strain curves could be input directly into LS-DYNA to define the material behavior. The LS-DYNA keyword MAT_LOW_ DENSITY_FOAM implements the constitutive model for this material. In tension, this material model assumes a linear elastic behavior until a particular defined tearing point. It should be noted that some of these foams are also highly strain rate dependent. However in the absence of experimental data, only one strain rate data was used. The comfort and energy absorbing liners were identified as a type of OCF and publicly available uniaxial compression tests results were used. The stress–strain curves were input directly into LS-DYNA. The foams were meshed using 8-noded hexahedral elements using 1-point integration (element formulation 1) in order to have a manageable number of elements, better control over the mesh quality, and prevent negative volumes in the elements due to the large deformations experienced in the analysis. The Headform: The headform shell was considered rigid because it was an approximation for the solid headform. The finite elements used were rigid 4-noded thin shell elements (Type 16) with one integration point through the thickness. The material for the headform is defined in the NOCSAE standard DOC (ND) 002 – 13 (NOCSAE 2013) where magnesium alloys are recommended because of their light weight and strength. The material model for this component was MAT_ELASTIC. For simplicity of the model, numerical stability, and better control of the contact initiated between the headform and soft foam, 4-noded thin quadrilateral elements were used. To define the interaction between the components, contact details are used in the finite element model. The comfort foam and energy foam as well as the outer shell
Shell foam max. acceleration (mm/ms2) 4.43 5.76 6.89
and the energy foam are coupled via tied contact. When defining automatic contact between two dissimilar materials such as the comfort foam and the magnesium headform, care had to be taken to see how the penalty function is implemented in contact. In our LS-DYNA model, the SOFT = 1 command is implemented which causes the contact stiffness to be determined based on stability considerations, taking into account the time step and nodal masses. Table 2 summarizes some of the details of the finite element model. 2.2. Helmet model numerical validation To ensure accuracy of the finite element results, a quality control step was implemented that included convergence analysis (Roache 1998) and monitoring some important energy-related parameters that are an integral part of a typical explicit finite element analysis (Bansal et al. 2009; Stahlecker et al. 2009; Deivanayagam et al. 2013). For example, the energy ratios are required to be between 0.9 and 1.1, the maximum hourglass energy ratio is expected to be below 0.1 etc. for the model results to be acceptable. Three simulations with varying mesh densities were completed to carry out the convergence analysis and select a model that would be used for the subsequent finite element analyses. The coarse mesh had 45,339 elements, the medium mesh had 84,008 elements, and the fine mesh had 205,402 elements. The response of the impactor and the helmet shell and hard foam were monitored (Figure 1(b)). For the impactor, the maximum acceleration of the center of gravity (CG) and the velocity of a corner node of the impactor were selected. For the helmet, acceleration of the nodes at the front edge of the helmet was used. The results are summarized in Table 3. The energy checks were all satisfied confirming that the finite element analysis performed with reasonable and acceptable accuracy. The energy ratio was between 0.9 and 1.1 for the simulations. The sliding energy ratio and hourglass energy ratio was 0.04 and 0.02, respectively. The kinetic energy ratio and internal energy ratio 0.99 and 0.92, respectively. 2.3. Helmet model experimental validation To compare the numerical model of the headform with experimental results, a drop test impacting the crown of the helmet was performed. The experimental setup
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The low frequency response shows that the model was able to recreate the salient features of the experimental acceleration profiles. The maximum acceleration for the simulation was 68.1 g and the average maximum acceleration for the experiments was 67.3 g with a standard deviation of 2.2 g. The maximum acceleration in the simulation occurred at 0.0131 s and the experiments averaged to 0.0139 s.
Figure 2. Drop test setup showing helmet mounted on Al-6061 headform and an ABS plastic cap. Y-Acceleration (Raw Data) vs Time Model Validation
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2.4. Human body model and injury thresholds
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was designed to be a reasonable approximation to the NOCSAE standard drop test system. The system is shown in Figure 2. In the test, a 5.95 kg block at 458.7 mm above the impact site was dropped to obtain an impact velocity of 3 m/s. An accelerometer was placed on the top of the impact plate to record the response of the system. The vertical (Y) acceleration of the impactor as obtained from the experiments was compared with the finite element model simulation as shown in Figures 3 (before filtering) and 4 (after filtering). The frequency content of the signal was determined by a fast Fourier t ransform (FFT) of the experimental signal. The FFT shows that the majority of the signal amplitude comes from the low frequency response.
The GHBMC full body model is a detailed finite element model (Chatelin et al. 2010; Bilston 2011; Mao et al. 2013). Supine magnetic resonance imaging and CT scans of an average adult male head were used to gather the skin surface, skull and facial bones, sinuses, cerebrum, cerebellum, lateral ventricles, corpus callosum, thalamus, brainstem, and cerebral white matter. Where anatomical features could not be defined with the imaging techniques, literature reviews were used to create the features – for example, differentiating the skull with outer cortical layer, middle cancellous layer, and inner cortical layer. The model has a total of 270,552 elements including 150,074 hexahedral elements, 352 pentahedral, 60,828 tetrahedral, 45,140 quadrilateral shell, 14,136 triangular shell, and 22 onedimensional beam elements. Brain tissue is a hydrated soft tissue that consists of 78% water that displays both elastic and viscous properties. As a result, the material properties of the head were determined by a large set of mechanical tests that have been performed on cadaver or animal specimens using compression, tension, shear, indentation, or magnetic resonance electrography methods. In summary, the gray matter and white matter were defined as linear viscoelastic materials with the white matter 25% stiffer than the gray. The cortical and cancellous bones were modeled with elastic-plastic materials, and the flesh was defined as viscoelastic material, which provides the best simulation robustness. The skin membranes, falx, tentorium, dura, arachnoid, and pia were defined as elastic materials.
3. Results With the combined finite element model (helmet plus GHBMC body model), it is now possible to compute the brain response in specific anatomical structures particularly relevant to mTBI. McAllister et al. (2011) showed that the maximum strain and strain rate fields in brain tissue during impact correlate with the changes in white matter integrity in the area of the corpus callosum. Therefore, the brain response data for the current study focuses on stress, strain and strain rate in the midbrain, corpus callosum, and the brain stem. Two load conditions were tested with
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Figure 4. Filtered experimental and simulation data for low frequency response (Y acceleration in impactor).
the helmet–human system – a frontal impact, defined by an impact angle of 30° with respect to the horizontal plane (Figure 6) and a crown impact (Figure 7) with the impactor velocity of 3 m/s. The loading conditions were not intended to replicate impacts that cause mTBI but were designed to replicate impacts that the NOCSAE standard deemed as dangerous impact conditions. We first investigate the extent of the deformations (resultant displacement) in the model as the impactcreated wave travels through the body. The finite element analyses were executed for a total time of 15 ms for crown
impact and for 30 ms for the oblique frontal impact. These time values were determined via trial-and-error to be adequate since the maximum response (principal stresses and strain, and stress and strain rates) occurs before that time value. Figure 5 shows the (final) state of the body at 15 ms and shows the time at which each identified node exceeded a deformation value of 0.25 mm, a value that is significantly smaller than the maximum absolute displacement of approximately 300 mm that is seen in the FE simulation. Figures 6 and 7 show the corpus callosum, midbrain, and brainstem highlighted in yellow, blue and green respectively inside the skull (not to be confused with parts of the helmet that are colored yellow and green) as they deform relative to the surrounding anatomical structures during the oblique frontal impact and crown impact, respectively. The relative resultant displacement versus time plots for corpus callosum, midbrain, and brainstem are shown in Figures 8 and 9, relative to the center of gravity (CG) of the skull. A positive displacement is when the item in question is moving faster than the CG. A qualitative assessment of the coup pressures can be made in various anatomical parts of the brain by looking at the relative magnitude of this displacement. The maximum principal and shear strains, strain rate, and stress values are shown in Figures 10–15 for the midbrain (MB), corpus callosum (CC) and brainstem (BS). Figures 10 and 11 show that the maximum principal strain due to frontal oblique impact condition is 8.9%
Figure 5. Displacement at time t = 15 ms for the crown impact model. Time values correspond to time when the resultant displacement is greater than 0.25 mm.
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Figure 6. Deformation of the human-helmet system during frontal oblique impact (time in ms).
Figure 7. Deformation of the human-helmet system during crown impact (time in ms).
and for the crown impact is 4.5% with both occurring in the brain-stem. While the strains doubled for the frontal oblique impact condition, they are still lower than the previously defined thresholds for brain injury (Zhang et al. 2004). Figures 12 and 13 show the maximum von Mises stress for the frontal oblique impact is 659 Pa and for the crown impact is 476 Pa with both occurring in the brain-stem. Figures 14 and 15 show that the maximum principal strain rate is 0.016 ms−1 for the front oblique impact and 0.027 ms−1 for the crown impact, both occurring in the brain-stem.
4. Discussions The integration of a full human body model in this study allows for an elimination of assumptions regarding the relationship between the head and the neck, and the neck’s relationship to the rest of the body. Simulation results in Figure 5 indicate that the backbone experiences the greatest deformation and the displacement wave reaches down to about the pelvis area of the full human body model indicating the need for including the torso in the analysis. The crown impact results in oscillatory displacements of brain tissue when subtracted from the rigid motion of the
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Figure 8. Frontal oblique impact displacement of corpus callosum, midbrain, and brainstem components.
Figure 11. Strain during crown impact.
Figure 12. Frontal impact maximum stress values. Figure 9. Crown impact displacement of corpus callosum, midbrain, and brainstem components.
Figure 10. Strain during frontal oblique impact.
Figure 13. Crown impact maximum stress values.
skull. A different phenomenon occurs with frontal oblique loading as shown in Figures 8 and 9. The corpus callosum is pushed toward the top of the skull whereas the midbrain and brainstem components are pulled toward the neck. Several publications mention injury thresholds for stress and strains in the brain due to impacts experienced during a game of football by analyzing concussion-causing impacts with validated finite element models of the brain (Willinger & Baumgartner 2003; Zhang et al. 2004). By analyzing head–head impact occurrences of mTBI with
a finite element model, Zhang predicted injury to occur with 50% probability at 7.8 kPa (von Mises) and principal strain of 0.19. Willinger and Baumgartner (2003) predicted injury at 18 kPa (von Mises) by analyzing brain tissue in car accidents with the finite element method and comparing the results against known injury cases. In-vitro testing performed by Pfister et al. (2003) to create mild to severe axonal injuries showed that axonal injury and neural cell death occur when applying principal strains from 20 to 70% and strain rates in the range of 20–90 s−1.
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Figure 14. Frontal impact maximum strain rate values.
for brain injury (Zhang et al. 2004). Not surprisingly, the maximum von Mises stresses (659 Pa for the frontal oblique and 476 Pa for the crown impact) also occur in the brain-stem region (Figures 12 and 13). However, they are a small fraction of the injury causing values reported by Willinger and Baumgartner (2003) and Zhang et al. (2004). However, the maximum strain rate values observed in the brain-stem in Figures 14 and 15 (16 and 27 s−1 for frontal oblique and crown impact, respectively) when compared against the thresholds for injury defined earlier show that the crown impact generates a potential injury inducing loading condition (Pfister et al. 2003) in the brain-stem and mid-brain. The maximum values of stress, principal strain, and principal strain rate in the brainstem illustrate an agreement with the clinical evaluations seen when studying patients who have experienced an mTBI. The brainstem is associated with regulating consciousness of the patient and so damage due to high strain-rates in that region could cause the patient to lose consciousness, which occurs in some cases for mTBI. Using this current model, the crown impact would be characterized as a potentially damaging loading condition due to the strain rates experienced in the brainstem and mid-brain. The maximum values of principal strain, shear strain, von Mises stress and strain rates are summarized in Tables 4 and 5.
Figure 15. Crown impact maximum strain rate values.
5. Concluding remarks
The maximal principal strains (of 8.9% under frontal oblique and 4.5% under crown impact) are observed in the brain-stem regions under both loading conditions followed closely by the mid-brain region (Figures 10 and 11). While the maximal principal strain doubled for the brainstem under the frontal oblique impact condition, they are still lower than the previously defined thresholds
An integrated human body–football helmet finite element model was created using the GHBMC human body model and analyzed using LS-DYNA. The Riddell Revolution AttackTM helmet was modeled with particular attention paid to its polycarbonate shell and bi-layer foam system. The finite element model was validated by comparing the performance of the model with experimental drop test. The integrated model was then created
Table 4. Maximum response values for crown impact. Max principal strain Max shear strain Strain rate (ms−1) Shear strain rate (ms−1) von Mises (Pa) Tresca (Pa)
Brainstem 0.045 0.044 0.027 0.027 476 274
Midbrain 0.045 0.037 0.019 0.018 345 196
Corpus callosum 0.023 0.021 0.0099 0.0097 131 76
Table 5. Maximum response values for frontal oblique impact. Maximum principal strain Maximum shear strain Strain rate (ms−1) Shear strain rate (ms−1) von Mises stress (Pa) Tresca stress (Pa)
Brainstem 0.088 0.08 0.016 0.017 659 380
Midbrain 0.029 0.028 0.017 0.016 443 253
Corpus callosum 0.076 0.073 0.0098 0.0082 291 166
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T. Darling et al.
by placing the helmet model over the skull portion of the GHBMC model. This model was then subjected to centric and non-centric impacts. A crown impact and a frontal oblique impact were performed and the strainrate, strain, and stress values experienced in the corpus callosum, midbrain, and brain stem were determined. The loading conditions were not intended to replicate impacts that cause mTBI but were designed to replicate impacts that the NOCSAE standard deemed as dangerous impact conditions. According to previously defined injury thresholds, the two loading conditions used in this study result in potential injury conditions through the high strain rates observed in the corpus callosum, midbrain, and brain stem. The coupled human-helmet system provides anatomical structure specific feedback during the occurrence of potential mTBI and helps establish a better understanding of the injury causing mechanisms. Moreover, the developed framework can potentially be used to study other helmet-related impact scenarios.
Acknowledgements The human body model was supplied to Arizona State University through the Global Human Body Modeling Consortium. The version used in this research is v4.1.1.
Disclosure statement No potential conflict of interest was reported by the authors.
Notes on contributors Tim Darling is currently a design engineer working for Honeywell Aerospace in Phoenix, AZ. He graduated from Arizona State University with a Master of Science degree in mechanical engineering. Jit Muthuswamy is an associate professor in the School of Biological and Health Systems Engineering at ASU. His research interests are in the areas of microelectromechanical systems (MEMS) for neural communication and plasticity in the central nervous system. His primary efforts are directed towards understanding and treating brain dysfunction. One of his main research thrusts is in the development of multi-functional neural prosthesis using MEMS technologies for precise tracking, communication, stimulation and control of neuronal function and dysfunction. Using these novel technologies in models of brain injury, he is interested in understanding the neurochemical and neuroelectrical dynamics that determine neurological outcome and the neuroprotective role of specific genes. Subramaniam Rajan is a professor of civil, mechanical and aerospace engineering in the School of Sustainable Engineering and the Built Environment. His research interests include development of constitutive models for composite materials, experimental techniques for the determination of material properties of composite materials, finite element analysis,
design optimization, and high-performance parallel computations. Using these tools, his research focus is on developing ballistic and blast mitigation solutions. He is the author of an undergraduate textbook on structural analysis and design, and a graduate book on object-oriented numerical analysis.
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