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Consequences of head size following trauma to the human head
Journal of Biomechanics 35 (2002) 153–160
Consequences of head size following trauma to the human head Svein Kleivena,*, Hans von Holsta,b a
Department of Aeronautics, Royal Institute of Technology, Teknikringen, 8 100 44 Stockholm, Sweden b Department of Clinical Neuroscience, Karolinska Institute, Stockholm, Sweden Accepted 25 September 2001
Abstract The objective of the present study was to evaluate whether variation of human head size results in different outcome regarding intracranial responses following a direct impact. Finite Element models representing different head sizes and with various element mesh densities were created. Frontal impacts towards padded surfaces as well as inertial loads were analyzed. The variation in intracranial stresses and intracranial pressures for different sizes of the geometry and for various element meshes were investigated. A significant correlation was found between experiment and simulation with regard to intracranial pressure characteristics. The maximal effective stresses in the brain increased more than a fourfold, from 3.6 kPa for the smallest head size to 16.3 kPa for the largest head size using the same acceleration impulse. When simulating a frontal impact towards a padding, the head injury criterion (HIC) value varies from the highest level of 2433 at a head mass of 2.34 kg to the lowest level of 1376 at a head mass of 5.98 kg, contradicting the increase in maximal intracranial stresses with head size. The conclusion is that the size dependence of the intracranial stresses associated with injury, is not predicted by the HIC. It is suggested that variations in head size should be considered when developing new head injury criteria. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Human head; Impact; Finite element analysis; Parametrization
1. Introduction The global burden of death due to accidents is ranked number nine in the list of the most frequent diseases in the world (Murray and Lopez, 1996). For people younger than 45 years the frequency of death or severe injury from road accidents is about six times higher than that from cancer. In Europe, road accidents are the second major cause of death, preceeded only by cancer (European Transport Safety Council, 1999). A significant number of road accidents affect the central nervous system in a devastating way by transferring high kinetic energy to the nervous tissue. The neuromechanic effects to the nervous tissue initiates a cascade of neurochemical steps often resulting in severe injuries, with a poor prognosis. The size of the human head varies within a wide range. Utilizating a parametrized geometry of an finite element (FE) model gives a tool for studying the effects *Corresponding author. Tel.: +46-8-790-6448; fax: +46-8-20-7865. E-mail address: svein@flyg.kth.se (S. Kleiven).
of these variations. A few studies have been performed regarding the size of the human head. In a study of cerebral concussion using subhuman primates, Ommaya et al. (1967) evaluated Holbourn’s scaling law in an effort to scale thresholds from primates to a concussion threshold for humans. In a two-dimensional (2D) numerical study by Prange et al. (1999), coronal rotational accelerations were used to evaluate differences in intracranial responses between adults and children. Kleinberger et al. (1998) discusses varying head criteria for the mid-sized male and the small-sized female dummies. However, the results were inconclusive and equal HIC limits are proposed. A parametrized and detailed 3D model of the human head has not previously been modeled and utilized for studying the effects of geometrical variations. A hypothesis is raised that following an impact, different sizes of the human head may result in varying intracranial responses of the brain tissue, and which might not be predicted by existing head injury criteria. The aim of the present study was to analyze the effect of different head sizes on impacts, and inertial loads with focus on stresses in the brain.
0021-9290/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 1 - 9 2 9 0 ( 0 1 ) 0 0 2 0 2 - 0
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S. Kleiven, H. von Holst / Journal of Biomechanics 35 (2002) 153–160
2. Methods The geometry of a male and a female human cadaver has been determined by CT, MR and sliced color photos. The geometric data are available through the visible human database (National Institute of Health) with a 0.3 mm incrementation in the coronal plane. The images were processed using the NIH Image 1.59 software (National Institute of Health, 1995). The 2D images (Fig. 1) are on an incremental basis used to generate a detailed 3D geometry. Points on the boundaries of the different tissues were determined and used to determine the lines and surfaces that define the geometry of the scalp, the skull, the dura, the brain tissue etc. Hereby a realistic skull thickness variation was achieved. This is an important feature as the
variation in skull thickness is significant, extending from the thick and porous frontal bone to the thin temporal bones. 2.1. Finite element mesh A FE-mesh was created of the three layers of the skull, facial bones, scalp, cerebrum, cerebellum, spinal cord, dura mater, tentorium and falx (Fig. 2). A simplified neck, including the extension of the brain stem to the spinal cord, dura mater, vertebrae and flesh, was also modeled. The non-linear dynamic FE code LSDYNA (Hallquist et al., 1999) was used for the analysis and post-processing. The inner and outer layer of compact bone of the three-layered skull, the facial bones, and the scalp were
Fig. 1. The scheme of creating a 3D FE-mesh from 2D images.
Fig. 2. FE-mesh.
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modeled by 4-node shell elements. The diplo.e layer of the cranium, and the tissues of the cerebrum, cerebellum and spinal cord were modeled by 8-node brick elements. The dura mater, tentorium and falx were modeled by 4node membrane elements. 2.2. Constitutive modeling To cope with the large elastic deformations, a Mooney-Rivlin hyperelastic constitutive law was utilized for the CNS tissues. This homogeneous, isotropic, non-linear and viscoelastic constitutive model was based on the work by Mendis et al. (1995). In addition, dissipative effects are taken into account through linear viscoelasticity by introducing viscous stress that is linearly related to the elastic stress. This law is given by C10 ðtÞ ¼ 0:9C01 ðtÞ ¼ 620:5 þ 1930et=0:008 þ 1103et=0:15 ðPaÞ 2.3. Incompressible material modeling In a conventional FE formulation, severe numerical difficulties are encountered for nearly incompressible materials because small volumetric strains cause large hydrostatic pressures due to the high effective bulk modulus. To circumvent this problem a displacementpressure (up) finite element formulation is used. This procedure features replacement of the pressure computed from the diplacement field by a separately interpolated pressure. To take into account the compressibility, a hydrostatic work term, WH ðJÞ; is included in the strain energy functional which is a function of the relative volume, J (Ogden, 1984) WðJ1 ; J2 ; JÞ ¼ C10 ðJ1 3Þ þ C01 ðJ2 3Þ þ WH ðJÞ; J1 ¼ I1 J 1=3 ; J2 ¼ I2 J 2=3 : In order to prevent volumetric work from contributing to the hydrostatic work, the first and second strain invariants are modified as shown. This procedure is described more in detail by Sussman and Bathe (1987). To reproduce the response of the human head when subjected to direct impact, a three-layered model is used for the skull. The material properties of cranial bone used in this study were based on McElhaney et al. (1970). The scalp and membranes were modeled with linear elastic characterization, using properties adopted from Melvin et al. (1970). 2.4. Material properties A summary of the properties used in this study is shown in Table 1.
Table 1 Properties used in FE study Tissue
Young’s modules (MPa)
Density (kg/dm3)
Poisson’s ratio
Outer table/face Inner table Diplo.e Neck bone Neck muscles Brain Dura mater Falx/tentorium Scalp
15 000 15 000 1000 1000 0.1 Hyperelastic 31.5 31.5 16.7
2.00 2.00 1.30 1.30 1.13 1.04 1.13 1.13 1.13
0.22 0.22 0.24 0.24 0.45 0.49999635 0.45 0.45 0.42
Poisson’s ratio for the brain was calculated using the initial and small strain approximation of Young’s modulus, E ¼ 6ðC10 þ C01 Þ; together with a bulk modulus of 2.1 GPa (McElhaney et al., 1976). Nevertheless, the numerical stability of the u/p-formulation gave only minor differences in the intracranial responses when varying the Poisson’s ratio between 0.4999 and 0.499999. 2.5. Interface conditions Based on the anatomy and physiology, the interface between the dura and the skull was modeled with a tied node contact definition in LS-DYNA. This contact algorithm uses a kinematic constraint method according to Hallquist et al. (1999). Because of the presence of CSF between the meningeal membranes and the brain, sliding contact definitions should be used for these interfaces, when large rotational loads are induced on the head. Several sliding contact definitions were compared with a tied contact definition. In order to model the foramen magnum interface in a realistic way, the upper part of the spinal cord was included in the model. Since the neck restraint is unlikely to affect the head response in a short duration (o6 ms) impact (Ruan et al., 1991), a free boundary condition was assumed in the analysis. 2.6. Parametrizing The spatial coordinates of points on the boundaries of the different tissues were scaled, respectively, in the same manner as described by Mertz et al. (1989). The inner and outer surfaces of the skull were scaled individually. In this way a detailed and parametrized model of the human head was created, which can be scaled with respect to the width, length, height and thickness of the skull as well as the overall size of the head and neck. The dimensions of the heads used in the analysis can be seen in Table 2.
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A study has been conducted on the dependence of the frontal and occipital pressure, the maximal shear stress and the maximal von Mises effective stress in the brain on the overall size (length, width and height) for an applied sinusoidal acceleration pulse similar to the one in the experimental validation. The equal acceleration pulse was applied to the rigidly modeled skull in the same direction as in the experimental validation, and as a half sinus with an amplitude of 2000 m/s2 and a duration of 5 ms. This gave an equal head injury criterion (HIC) value of about 960 to all the different head sizes. In addition, the head models were impacted frontally with a velocity of 5 m/s towards a padded surface to simulate a more realistic accident scenario. The head length, width and height were scaled to fit the percentiles for British adults according to Pheasant (1996). To take into account differences in populations, and the secular trend of an increase in adult stature, two models representing an exceptionally small adult female, and an extremely large man were added to the analysis. 2.7. Experimental validation Results from simulations with the FE model were compared with the intracranial pressure-time recordings from experiments conducted by Nahum et al. (1977) (Fig. 3) (see Webpage of the Journal of Biomechanics: http//www.elsevier. com/locate/jbiomech for animations of pressure distribution during an impact). In these
Table 2 Size parameters Head model
Mass (kg)
Width (mm)
Length (mm)
Small female 5th perc. female 50th perc. female 50th perc. male 95th perc. male Large male
2.34 2.93 3.64 4.44 5.35 5.98
125 135 145 155 165 180
150 165 180 195 210 230
experiments cadaver heads were impacted to the frontal bone by a cylindrical load cell with a circular contact area. To increase the duration of the impact, Nahum et al. placed various paddings between the impactor and the scalp. The geometry and size of the impactor (60 cylindrical load cell), and the approximate thickness and type of padding material was found and modeled. The padding on the impactor was modeled with a foam material model. The properties of the padding was adjusted so that the force vs time and acceleration characteristics of the experiment was largely reproduced. A coefficient of friction of 0.3 was used between the padding and the head. The dependence of the mesh density on the intracranial pressure at frontal and occipital locations in the experiments performed by Nahum et al. (1977) was studied. A model with parametrized mesh density was created, and the dependence on the element size was studied. Four models, each with different element sizes, were created. The number of elements ranged from 1500, in the coarsely meshed model, to about 40 000 in the most refined model.
3. Results When comparison was made between earlier experiments and the present FE model, a significant correlation could be seen (Fig. 4). The calculated pressure–time curves correlate reasonably well with the experimental ones for all locations (Fig. 5). It was found that both the maximal effective (von Mises) stress and the maximal shear stress, as well as the magnitudes of the frontal and occipital pressures in the brain increases with increasing overall size of the head (Fig. 6), when using the same acceleration pulse (i.e. same HIC). This supports the hypothesis of varying intracranial response for different sizes of the human head. When simulating a frontal impact towards a
Fig. 3. Simulation of experiments conducted by Nahum et al. (1977) (left) and pressure distribution at 3 ms (right).
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Fig. 4. Correlation between earlier experiments and present FE simulation. Force vs time (left) and head acceleration vs time (right).
Fig. 5. Simulation of intracranial pressure characteristics.
Fig. 6. Dependence of the intracranial stress and pressure on head size using the same acceleration impulse: (A) the effective (von Mises) stress varies from 3.6 to 16.3 kPa, and the shear stress varies from 2.1 to 9.4 kPa; (B) the frontal pressure ranges between 160.0 and 255.5 kPa, while the occipital pressure varies from 284.9 to 114.0 kPa.
padding, a further confirmation of this phenomenon can be seen (Fig. 7). Interestingly, this cannot be predicted by existing head injury criteria; the HIC value decreases with increasing head size while the maximal intracranial stresses increases.
From the study of the dependence on the element sizes, it was found that the magnitudes of both the frontal and the occipital pressures converge towards the experimental values when the number of elements exceeded about 7500.
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Fig. 7. Dependence of the intracranial stress and HIC-value on head size when enduring frontal impact towards padding: (A) the effective (von Mises) stress varies from 4.4 to 15.1 kPa, and the shear stress varies from 2.5 to 8.7 kPa; (B) the HIC-value ranges between 1376 and 2433.
4. Discussion The present results verify the hypothesis that variation in head size alter the outcome of an impact. Based on this FE model new head injury criteria for both adult males as well as females (within certain percentiles when it comes to geometry) can be evaluated. In this respect, the injury criteria are valid for a larger span of the population. Today, injury criteria evaluated by FEM are based on average models, but in real life and as indicated by the anthropometric study, the worst case might not be the 50th percentile. Numerous FE models of the human head such as Bandak et al. (1994), Zhou et al. (1995), Ruan et al. (1997), Claessens et al. (1997), Willinger et al. (1999) and Kuijpers et al. (1995) (among others), have been validated against the experiments of Nahum et al. (1977). These models and other state of the art 3D FE models of the human head have all assumed isotropic, linear elastic or linear viscoelastic and homogeneous material properties within each modeled component. Biological materials do not follow the constitutive relations for common engineering materials. A biological material is often anisotropic, inhomogeneous, nonlinear and viscoelastic. In addition, there is a great variability between different individuals. The assumption of linear elasticity or viscoelasticity is a great limitation, especially in CNS tissue modeling, due to its typical non-linear behavior and also because it is often enduring large deformations during impacts and accelerations of the head. Thus, a hyperelastic and viscoelastic constitutive law was used. In combination with the incompressible finite element formulation, this gives an accurate correlation between experiments and simulations. To further increase accuracy, the actual geometry of the specimen (overall length, width and height) was reproduced according to the measurements of Nahum et al. (1977).
The penalty contact algorithm was found to be insufficient for the brain–membrane interfaces. A gap was created at the contrecoup region because of the ability of only transferring loads in compression. Hence, a tied node contact algorithm which transfers load even in tension, was implemented. Large relative motion is not allowed between the skull and the brain but a tensile load is possible at the contrecoup region. This gave a more accurate representation of magnitudes and characteristics of the pressure–time for the occipital region. The skull–brain interface contains, in addition to CSF, also bridging veins and arachnoidal trabeculations that limit this interface in the radial direction and motivates usage of a tied interface. For large rotational loads, on the other hand, a contact definition that can transfer loads in tension as well as permits large relative motion between the skull and the brain should be preferred. However, in the simulation of the experiment, a slight variation in the time duration is experienced for both the pressures and the acceleration. This might in part be explained by the influence of the neck constraint, which in this case was assumed to be free. Also, access to the exact data of the padding used in the experiments would probably improve the predictions. A further difficulty experienced by Nahum et al. (1977), when conducting the experiments, was the presence of motion in the lateral direction. To minimize this out of plane motion, sutures were attached to the ears of the test subjects prior to impact. This (although minimized) lateral motion, as well as the influence of the sutures, would probably also affect the results, and are not accounted for in the simulations. The accuracy of an FE model is significantly dependent on its discretization. It can only be speculated to what extent the present FE model describes the complex geometry of the human head. This depends largely on how many elements are used to describe the complex boundaries and surfaces. As presented in the
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results, the model prediction becomes more accurate with smaller elements. In the future, when the computer speed increases, further improvements can be accomplished with this model because the mapped meshing gives a flexible number of elements. The present paper shows that a non-linear and viscoelastic constitutive law together with a displacement–pressure element formulation for the CNS tissues gives significant correlation with experiments. The maximal shear stress and maximal effective stress, as well as the magnitudes of the frontal and occipital pressures in the brain increase with increasing overall size of the head when enduring the same acceleration pulse, i.e. the same HIC value. When impacted frontally towards a padding, the HIC value decreases with increasing head size, contradicting the findings of increasing intracranial stresses with increasing head size. Currently, mass and geometrical scaling relationships are used to scale 50th percentile dummies to other sizes. Such a procedure was used for the scaling of the spatial coordinates in the present study. Mertz (1984) proposed scaling factors for the resulting force–time response following an impact. The scaling factors were based on the differential equations of a simple spring–mass system. Applying the normalizing factor for the force indicates an increase in impact force by head size, which was also experienced in the present study. For the intracranial response, no normalizing procedures exist today. The current results implies that a reduced HIC value should be used when analyzing data from dummies larger than 50th percentile. Correspondingly, a higher HIC value could be allowed for dummies of smaller size. In the discussion of various criteria for different head sizes of crash dummies, Kleinberger et al. (1998) proposed equal HIC limits for mid-sized males and small females, solely based on geometric scaling and the hypothesis that small females would have lower modulus and strength of the cranial bones than a 50th percentile man. As mentioned in this study, data comparing the modulus and strength of female anatomic structures to male are not available. It can therefore only be hypothesized to which extent and significance any such difference would play a role in prediction of traumatic head injuries. When Margulies and Thibault (1992) proposed a tolerance criterion for DAI they approximated the head as an infinite cylinder using a linearly viscoelastic constitutive model for the brain. In that study, it was found that the maximum shear strain in the central parts of the cylinder increased with increasing size, which supports the findings in the present study. It is concluded that the size dependence of the intracranial stresses associated with injury, is not predicted by the HIC. It is also suggested that variations
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in head size should be considered when developing new head injury criteria.
Acknowledgements This work was supported by the Swedish Transport & Communications Research Board, Dnr. 1999-0847 and the Foundation of Neurotraumatologic Research and Development.
References Bandak, F.A., et al., 1994. A three-dimensional FE analysis of the human brain under combined rotational and translational accelerations. In: Proceedings of the 38th Stapp Car Crash Conference, Society of Automotive Engineers, pp.145–163. Claessens, M., et al., 1997. Modeling of the human head under impact conditions: a parametric study. In: Proceedings of the 41st Stapp Car Crash Conference, SAE Paper No. 973338. Society of Automotive Engineers, pp. 315–328. European Transport Safety Council, 1999. Reducing the severity of road injuries through post impact care. ISBN: 90-76024-07-3. Hallquist, J.O., et al., 1999. LS-DYNA KEYWORD USER’S MANUAL & Theoretical Manual, Version 950 Livermore Software Technology Corporation. Kleinberger, M., et al., 1998. Development of improved injury criteria for the assessment of advanced automotive restraint systems. National Highway Traffic Safety Administration. http:// www.nrd.nhtsa. dot.gov/pdf/nrd-11/airbags/criteria. pdf. Kuijpers, A.H.W.M., et al., 1995. The influence of different boundary conditions on the response of the head to impact: a’ twodimensional finite element study. Journal of Neurotraumatology 12 (4), 715–724. Margulies, S.S., Thibault, L.E., 1992. A proposed tolerance criterion for diffuse axonal injury in man. Journal of Biomechanics 25 (8), 917–923. McElhaney, J.H., et al., 1970. Mechanical properties of cranial bone. Journal of Biomechanics 3, 495–511. McElhaney J.H., et al., 1976. Handbook of Human Tolerance. Japan Automobile Research Institute Inc., Tokyo, p.143. Melvin J. W., et al., 1970. Development of a mechanical model of the human headFdetermination of tissue properties and synthetic substitute materials. 14th Stapp Car Crash Conference, SAE Paper No. 700903. Society of Automotive Engineers. Mendis, K.K., et al., 1995. A constitutive relationship for large deformation finite element modeling of brain tissue. Journal of Biomechanical Engineering 117 (4), 279–285. Merz, H.J., et al., 1984. A procedure for normalizing impact response data, SAE Paper No. 840884. Society of Automotive Engineers pp. 4351–4358. Merz, H.J., et al., 1989. Size, weight and biomechanical impact response requirements for adult size small female and large male dummies. In: SP-782-Automotive Frontal Impacts, SAE Paper No. 890756. Society of Automotive Engineers pp. 133–144. Murray, C.J.L., Lopez, A.D., 1996. The Global Burden of DiseaseSummary. The Harvard School of Public Health, Harvard Univeristy Press, Cambridge, MA, p. 43. Nahum, A.M., et al., 1977. Intracranial pressure dynamics during head impact. In: Proceedings of the 21st Stapp Car Crash Conference, SAE Paper No. 770922. Society of Automotive Engineers.
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National Institute of Health (NIH), National Institute of Mental Health (NIMH), Research Services Branch (RSB), 1995. NIH Image, a public domain image processing and analysis program for the Macintosh: http://rsb.info.nih.gov/ National Institutes of Health (NIH), U.S. National Library of Medicine, Department of Health & Human Services. Visible Human Database: www.nlm.nih.gov/research/visible/visible\ human.html. Ogden, R.W, 1984. Non-Linear Elastic Deformations.. Dover Publications Inc., Mineola, NY. Ommaya, A.K., et al., 1967. Scaling of experimental data on cerebral concussion in sub-human primates to concussion threshold for man, SAE Paper No. 670906. Society of Automative Engineers, pp. 73–80. Pheasant, S., 1996. Bodyspace, Anthropometry, Ergonomics and the Design of Work, 2nd Edition. Taylor & Francis, London. Prange, M.T., et al., 1999. Pediatric rotational inertial brain injury: the relative influence of brain size and mechanical properties, 43rd
Stapp Car Crash Conference, SAE Paper No. 99SC23. Society of Automotive Engineers. Ruan, J.S., et al., 1991. Human head dynamic response to side impact by finite element modeling. Transactions of the ASME 113, 276–283. Ruan, J.S., et al., 1997. Impact head injury analysis using an explicit finite element human head model. Journal of Traffic Medicine 25, 33–40. Sussman, T., Bathe, K.J., 1987. A finite element formulation for nonlinear incompressible elastic and inelastic analysis. Computers & Structres 26 (1/2), 357–409. Willinger, R., et al., 1999. Three-dimensional human head finiteelement model validation against two experimental impacts. Annals of Biomedical Engineering 27, 403–410. Zhou, C., et al., 1995. A new model comparing impact responses of the homogeneous and inhomogeneous human brain. In: Proceedings of the 39th Stapp Car Crash Conference, Society of Automotive Engineers, pp. 121–137.
Consequences of head size following trauma to the human head Svein Kleivena,*, Hans von Holsta,b a
Department of Aeronautics, Royal Institute of Technology, Teknikringen, 8 100 44 Stockholm, Sweden b Department of Clinical Neuroscience, Karolinska Institute, Stockholm, Sweden Accepted 25 September 2001
Abstract The objective of the present study was to evaluate whether variation of human head size results in different outcome regarding intracranial responses following a direct impact. Finite Element models representing different head sizes and with various element mesh densities were created. Frontal impacts towards padded surfaces as well as inertial loads were analyzed. The variation in intracranial stresses and intracranial pressures for different sizes of the geometry and for various element meshes were investigated. A significant correlation was found between experiment and simulation with regard to intracranial pressure characteristics. The maximal effective stresses in the brain increased more than a fourfold, from 3.6 kPa for the smallest head size to 16.3 kPa for the largest head size using the same acceleration impulse. When simulating a frontal impact towards a padding, the head injury criterion (HIC) value varies from the highest level of 2433 at a head mass of 2.34 kg to the lowest level of 1376 at a head mass of 5.98 kg, contradicting the increase in maximal intracranial stresses with head size. The conclusion is that the size dependence of the intracranial stresses associated with injury, is not predicted by the HIC. It is suggested that variations in head size should be considered when developing new head injury criteria. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Human head; Impact; Finite element analysis; Parametrization
1. Introduction The global burden of death due to accidents is ranked number nine in the list of the most frequent diseases in the world (Murray and Lopez, 1996). For people younger than 45 years the frequency of death or severe injury from road accidents is about six times higher than that from cancer. In Europe, road accidents are the second major cause of death, preceeded only by cancer (European Transport Safety Council, 1999). A significant number of road accidents affect the central nervous system in a devastating way by transferring high kinetic energy to the nervous tissue. The neuromechanic effects to the nervous tissue initiates a cascade of neurochemical steps often resulting in severe injuries, with a poor prognosis. The size of the human head varies within a wide range. Utilizating a parametrized geometry of an finite element (FE) model gives a tool for studying the effects *Corresponding author. Tel.: +46-8-790-6448; fax: +46-8-20-7865. E-mail address: svein@flyg.kth.se (S. Kleiven).
of these variations. A few studies have been performed regarding the size of the human head. In a study of cerebral concussion using subhuman primates, Ommaya et al. (1967) evaluated Holbourn’s scaling law in an effort to scale thresholds from primates to a concussion threshold for humans. In a two-dimensional (2D) numerical study by Prange et al. (1999), coronal rotational accelerations were used to evaluate differences in intracranial responses between adults and children. Kleinberger et al. (1998) discusses varying head criteria for the mid-sized male and the small-sized female dummies. However, the results were inconclusive and equal HIC limits are proposed. A parametrized and detailed 3D model of the human head has not previously been modeled and utilized for studying the effects of geometrical variations. A hypothesis is raised that following an impact, different sizes of the human head may result in varying intracranial responses of the brain tissue, and which might not be predicted by existing head injury criteria. The aim of the present study was to analyze the effect of different head sizes on impacts, and inertial loads with focus on stresses in the brain.
0021-9290/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 1 - 9 2 9 0 ( 0 1 ) 0 0 2 0 2 - 0
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2. Methods The geometry of a male and a female human cadaver has been determined by CT, MR and sliced color photos. The geometric data are available through the visible human database (National Institute of Health) with a 0.3 mm incrementation in the coronal plane. The images were processed using the NIH Image 1.59 software (National Institute of Health, 1995). The 2D images (Fig. 1) are on an incremental basis used to generate a detailed 3D geometry. Points on the boundaries of the different tissues were determined and used to determine the lines and surfaces that define the geometry of the scalp, the skull, the dura, the brain tissue etc. Hereby a realistic skull thickness variation was achieved. This is an important feature as the
variation in skull thickness is significant, extending from the thick and porous frontal bone to the thin temporal bones. 2.1. Finite element mesh A FE-mesh was created of the three layers of the skull, facial bones, scalp, cerebrum, cerebellum, spinal cord, dura mater, tentorium and falx (Fig. 2). A simplified neck, including the extension of the brain stem to the spinal cord, dura mater, vertebrae and flesh, was also modeled. The non-linear dynamic FE code LSDYNA (Hallquist et al., 1999) was used for the analysis and post-processing. The inner and outer layer of compact bone of the three-layered skull, the facial bones, and the scalp were
Fig. 1. The scheme of creating a 3D FE-mesh from 2D images.
Fig. 2. FE-mesh.
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modeled by 4-node shell elements. The diplo.e layer of the cranium, and the tissues of the cerebrum, cerebellum and spinal cord were modeled by 8-node brick elements. The dura mater, tentorium and falx were modeled by 4node membrane elements. 2.2. Constitutive modeling To cope with the large elastic deformations, a Mooney-Rivlin hyperelastic constitutive law was utilized for the CNS tissues. This homogeneous, isotropic, non-linear and viscoelastic constitutive model was based on the work by Mendis et al. (1995). In addition, dissipative effects are taken into account through linear viscoelasticity by introducing viscous stress that is linearly related to the elastic stress. This law is given by C10 ðtÞ ¼ 0:9C01 ðtÞ ¼ 620:5 þ 1930et=0:008 þ 1103et=0:15 ðPaÞ 2.3. Incompressible material modeling In a conventional FE formulation, severe numerical difficulties are encountered for nearly incompressible materials because small volumetric strains cause large hydrostatic pressures due to the high effective bulk modulus. To circumvent this problem a displacementpressure (up) finite element formulation is used. This procedure features replacement of the pressure computed from the diplacement field by a separately interpolated pressure. To take into account the compressibility, a hydrostatic work term, WH ðJÞ; is included in the strain energy functional which is a function of the relative volume, J (Ogden, 1984) WðJ1 ; J2 ; JÞ ¼ C10 ðJ1 3Þ þ C01 ðJ2 3Þ þ WH ðJÞ; J1 ¼ I1 J 1=3 ; J2 ¼ I2 J 2=3 : In order to prevent volumetric work from contributing to the hydrostatic work, the first and second strain invariants are modified as shown. This procedure is described more in detail by Sussman and Bathe (1987). To reproduce the response of the human head when subjected to direct impact, a three-layered model is used for the skull. The material properties of cranial bone used in this study were based on McElhaney et al. (1970). The scalp and membranes were modeled with linear elastic characterization, using properties adopted from Melvin et al. (1970). 2.4. Material properties A summary of the properties used in this study is shown in Table 1.
Table 1 Properties used in FE study Tissue
Young’s modules (MPa)
Density (kg/dm3)
Poisson’s ratio
Outer table/face Inner table Diplo.e Neck bone Neck muscles Brain Dura mater Falx/tentorium Scalp
15 000 15 000 1000 1000 0.1 Hyperelastic 31.5 31.5 16.7
2.00 2.00 1.30 1.30 1.13 1.04 1.13 1.13 1.13
0.22 0.22 0.24 0.24 0.45 0.49999635 0.45 0.45 0.42
Poisson’s ratio for the brain was calculated using the initial and small strain approximation of Young’s modulus, E ¼ 6ðC10 þ C01 Þ; together with a bulk modulus of 2.1 GPa (McElhaney et al., 1976). Nevertheless, the numerical stability of the u/p-formulation gave only minor differences in the intracranial responses when varying the Poisson’s ratio between 0.4999 and 0.499999. 2.5. Interface conditions Based on the anatomy and physiology, the interface between the dura and the skull was modeled with a tied node contact definition in LS-DYNA. This contact algorithm uses a kinematic constraint method according to Hallquist et al. (1999). Because of the presence of CSF between the meningeal membranes and the brain, sliding contact definitions should be used for these interfaces, when large rotational loads are induced on the head. Several sliding contact definitions were compared with a tied contact definition. In order to model the foramen magnum interface in a realistic way, the upper part of the spinal cord was included in the model. Since the neck restraint is unlikely to affect the head response in a short duration (o6 ms) impact (Ruan et al., 1991), a free boundary condition was assumed in the analysis. 2.6. Parametrizing The spatial coordinates of points on the boundaries of the different tissues were scaled, respectively, in the same manner as described by Mertz et al. (1989). The inner and outer surfaces of the skull were scaled individually. In this way a detailed and parametrized model of the human head was created, which can be scaled with respect to the width, length, height and thickness of the skull as well as the overall size of the head and neck. The dimensions of the heads used in the analysis can be seen in Table 2.
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A study has been conducted on the dependence of the frontal and occipital pressure, the maximal shear stress and the maximal von Mises effective stress in the brain on the overall size (length, width and height) for an applied sinusoidal acceleration pulse similar to the one in the experimental validation. The equal acceleration pulse was applied to the rigidly modeled skull in the same direction as in the experimental validation, and as a half sinus with an amplitude of 2000 m/s2 and a duration of 5 ms. This gave an equal head injury criterion (HIC) value of about 960 to all the different head sizes. In addition, the head models were impacted frontally with a velocity of 5 m/s towards a padded surface to simulate a more realistic accident scenario. The head length, width and height were scaled to fit the percentiles for British adults according to Pheasant (1996). To take into account differences in populations, and the secular trend of an increase in adult stature, two models representing an exceptionally small adult female, and an extremely large man were added to the analysis. 2.7. Experimental validation Results from simulations with the FE model were compared with the intracranial pressure-time recordings from experiments conducted by Nahum et al. (1977) (Fig. 3) (see Webpage of the Journal of Biomechanics: http//www.elsevier. com/locate/jbiomech for animations of pressure distribution during an impact). In these
Table 2 Size parameters Head model
Mass (kg)
Width (mm)
Length (mm)
Small female 5th perc. female 50th perc. female 50th perc. male 95th perc. male Large male
2.34 2.93 3.64 4.44 5.35 5.98
125 135 145 155 165 180
150 165 180 195 210 230
experiments cadaver heads were impacted to the frontal bone by a cylindrical load cell with a circular contact area. To increase the duration of the impact, Nahum et al. placed various paddings between the impactor and the scalp. The geometry and size of the impactor (60 cylindrical load cell), and the approximate thickness and type of padding material was found and modeled. The padding on the impactor was modeled with a foam material model. The properties of the padding was adjusted so that the force vs time and acceleration characteristics of the experiment was largely reproduced. A coefficient of friction of 0.3 was used between the padding and the head. The dependence of the mesh density on the intracranial pressure at frontal and occipital locations in the experiments performed by Nahum et al. (1977) was studied. A model with parametrized mesh density was created, and the dependence on the element size was studied. Four models, each with different element sizes, were created. The number of elements ranged from 1500, in the coarsely meshed model, to about 40 000 in the most refined model.
3. Results When comparison was made between earlier experiments and the present FE model, a significant correlation could be seen (Fig. 4). The calculated pressure–time curves correlate reasonably well with the experimental ones for all locations (Fig. 5). It was found that both the maximal effective (von Mises) stress and the maximal shear stress, as well as the magnitudes of the frontal and occipital pressures in the brain increases with increasing overall size of the head (Fig. 6), when using the same acceleration pulse (i.e. same HIC). This supports the hypothesis of varying intracranial response for different sizes of the human head. When simulating a frontal impact towards a
Fig. 3. Simulation of experiments conducted by Nahum et al. (1977) (left) and pressure distribution at 3 ms (right).
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Fig. 4. Correlation between earlier experiments and present FE simulation. Force vs time (left) and head acceleration vs time (right).
Fig. 5. Simulation of intracranial pressure characteristics.
Fig. 6. Dependence of the intracranial stress and pressure on head size using the same acceleration impulse: (A) the effective (von Mises) stress varies from 3.6 to 16.3 kPa, and the shear stress varies from 2.1 to 9.4 kPa; (B) the frontal pressure ranges between 160.0 and 255.5 kPa, while the occipital pressure varies from 284.9 to 114.0 kPa.
padding, a further confirmation of this phenomenon can be seen (Fig. 7). Interestingly, this cannot be predicted by existing head injury criteria; the HIC value decreases with increasing head size while the maximal intracranial stresses increases.
From the study of the dependence on the element sizes, it was found that the magnitudes of both the frontal and the occipital pressures converge towards the experimental values when the number of elements exceeded about 7500.
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Fig. 7. Dependence of the intracranial stress and HIC-value on head size when enduring frontal impact towards padding: (A) the effective (von Mises) stress varies from 4.4 to 15.1 kPa, and the shear stress varies from 2.5 to 8.7 kPa; (B) the HIC-value ranges between 1376 and 2433.
4. Discussion The present results verify the hypothesis that variation in head size alter the outcome of an impact. Based on this FE model new head injury criteria for both adult males as well as females (within certain percentiles when it comes to geometry) can be evaluated. In this respect, the injury criteria are valid for a larger span of the population. Today, injury criteria evaluated by FEM are based on average models, but in real life and as indicated by the anthropometric study, the worst case might not be the 50th percentile. Numerous FE models of the human head such as Bandak et al. (1994), Zhou et al. (1995), Ruan et al. (1997), Claessens et al. (1997), Willinger et al. (1999) and Kuijpers et al. (1995) (among others), have been validated against the experiments of Nahum et al. (1977). These models and other state of the art 3D FE models of the human head have all assumed isotropic, linear elastic or linear viscoelastic and homogeneous material properties within each modeled component. Biological materials do not follow the constitutive relations for common engineering materials. A biological material is often anisotropic, inhomogeneous, nonlinear and viscoelastic. In addition, there is a great variability between different individuals. The assumption of linear elasticity or viscoelasticity is a great limitation, especially in CNS tissue modeling, due to its typical non-linear behavior and also because it is often enduring large deformations during impacts and accelerations of the head. Thus, a hyperelastic and viscoelastic constitutive law was used. In combination with the incompressible finite element formulation, this gives an accurate correlation between experiments and simulations. To further increase accuracy, the actual geometry of the specimen (overall length, width and height) was reproduced according to the measurements of Nahum et al. (1977).
The penalty contact algorithm was found to be insufficient for the brain–membrane interfaces. A gap was created at the contrecoup region because of the ability of only transferring loads in compression. Hence, a tied node contact algorithm which transfers load even in tension, was implemented. Large relative motion is not allowed between the skull and the brain but a tensile load is possible at the contrecoup region. This gave a more accurate representation of magnitudes and characteristics of the pressure–time for the occipital region. The skull–brain interface contains, in addition to CSF, also bridging veins and arachnoidal trabeculations that limit this interface in the radial direction and motivates usage of a tied interface. For large rotational loads, on the other hand, a contact definition that can transfer loads in tension as well as permits large relative motion between the skull and the brain should be preferred. However, in the simulation of the experiment, a slight variation in the time duration is experienced for both the pressures and the acceleration. This might in part be explained by the influence of the neck constraint, which in this case was assumed to be free. Also, access to the exact data of the padding used in the experiments would probably improve the predictions. A further difficulty experienced by Nahum et al. (1977), when conducting the experiments, was the presence of motion in the lateral direction. To minimize this out of plane motion, sutures were attached to the ears of the test subjects prior to impact. This (although minimized) lateral motion, as well as the influence of the sutures, would probably also affect the results, and are not accounted for in the simulations. The accuracy of an FE model is significantly dependent on its discretization. It can only be speculated to what extent the present FE model describes the complex geometry of the human head. This depends largely on how many elements are used to describe the complex boundaries and surfaces. As presented in the
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results, the model prediction becomes more accurate with smaller elements. In the future, when the computer speed increases, further improvements can be accomplished with this model because the mapped meshing gives a flexible number of elements. The present paper shows that a non-linear and viscoelastic constitutive law together with a displacement–pressure element formulation for the CNS tissues gives significant correlation with experiments. The maximal shear stress and maximal effective stress, as well as the magnitudes of the frontal and occipital pressures in the brain increase with increasing overall size of the head when enduring the same acceleration pulse, i.e. the same HIC value. When impacted frontally towards a padding, the HIC value decreases with increasing head size, contradicting the findings of increasing intracranial stresses with increasing head size. Currently, mass and geometrical scaling relationships are used to scale 50th percentile dummies to other sizes. Such a procedure was used for the scaling of the spatial coordinates in the present study. Mertz (1984) proposed scaling factors for the resulting force–time response following an impact. The scaling factors were based on the differential equations of a simple spring–mass system. Applying the normalizing factor for the force indicates an increase in impact force by head size, which was also experienced in the present study. For the intracranial response, no normalizing procedures exist today. The current results implies that a reduced HIC value should be used when analyzing data from dummies larger than 50th percentile. Correspondingly, a higher HIC value could be allowed for dummies of smaller size. In the discussion of various criteria for different head sizes of crash dummies, Kleinberger et al. (1998) proposed equal HIC limits for mid-sized males and small females, solely based on geometric scaling and the hypothesis that small females would have lower modulus and strength of the cranial bones than a 50th percentile man. As mentioned in this study, data comparing the modulus and strength of female anatomic structures to male are not available. It can therefore only be hypothesized to which extent and significance any such difference would play a role in prediction of traumatic head injuries. When Margulies and Thibault (1992) proposed a tolerance criterion for DAI they approximated the head as an infinite cylinder using a linearly viscoelastic constitutive model for the brain. In that study, it was found that the maximum shear strain in the central parts of the cylinder increased with increasing size, which supports the findings in the present study. It is concluded that the size dependence of the intracranial stresses associated with injury, is not predicted by the HIC. It is also suggested that variations
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in head size should be considered when developing new head injury criteria.
Acknowledgements This work was supported by the Swedish Transport & Communications Research Board, Dnr. 1999-0847 and the Foundation of Neurotraumatologic Research and Development.
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