Head and brain response to blast using sagittal and transverse finite element models.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING Int. J. Numer. Meth. Biomed. Engng. 2014; 30:470–489 Published online 30 November 2013 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/cnm.2612

Head and brain response to blast using sagittal and transverse finite element models Dilaver Singh* ,† , Duane S. Cronin and Tyler N. Haladuick University of Waterloo, Waterloo, ON, Canada

SUMMARY Mild traumatic brain injury caused by blast exposure from Improvised Explosive Devices has become increasingly prevalent in modern conflicts. To investigate head kinematics and brain tissue response in blast scenarios, two solid hexahedral blast-head models were developed in the sagittal and transverse planes. The models were coupled to an Arbitrary Lagrangian-Eulerian model of the surrounding air to model blast-head interaction, for three blast load cases (5 kg C4 at 3, 3.5 and 4 m). The models were validated using experimental kinematic data, where predicted accelerations were in good agreement with experimental tests, and intracranial pressure traces at four locations in the brain, where the models provided good predictions for frontal, temporal and parietal, but underpredicted pressures at the occipital location. Brain tissue response was investigated for the wide range of constitutive properties available. The models predicted relatively low peak principal brain tissue strains from 0.035 to 0.087; however, strain rates ranged from 225 to 571 s-1. Importantly, these models have allowed us to quantify expected strains and strain rates experienced in brain tissue, which can be used to guide future material characterization. These computationally efficient and predictive models can be used to evaluate protection and mitigation strategies in future analysis. Copyright © 2013 John Wiley & Sons, Ltd. Received 14 November 2012; Revised 8 October 2013; Accepted 12 October 2013 KEY WORDS:

blast; finite element modeling; mild traumatic brain injury; head and brain modeling

1. INTRODUCTION Mild traumatic brain injury has become increasingly prevalent in modern military conflicts and is attributed to blast exposure from Improvised Explosive Devices [1]. This has prompted significant research towards understanding blast injuries to the head, with the ultimate goal of injury mitigation. Predicting brain injury caused by blast is challenging because of the complex nature of blast loads, as well as the limited understanding of brain tissue injury mechanisms. Finite element models have been used for decades to predict tissue response to applied load and investigate potential for injury [2]. In contrast to automotive or sports impacts, blast loads are dominated by pressure wave dynamics, so finite element models that simulate blast interaction with the head require relatively small elements to model wave propagation accurately [3]. Pressure transients are smeared over a few element lengths in explicit finite element codes and coarse elements underpredict peak pressures. Because of the need for a large air mesh in blast simulations, a full three-dimensional (3D) model of the head with an appropriate level of mesh refinement results in a computationally prohibitive model. This has previously been estimated to require approximately 16 million elements with solver times over 300 h per model for the human head. Although this may seem feasible for a small number of simulations, model development and validation often requires tens to hundreds of analyses and would not be reasonable with currently available computing power. *Correspondence to: Dilaver Singh, Department of Mechanical Engineering, University of Waterloo, 200 University Ave. West, Waterloo, ON, Canada, N2L 3G1. † E-mail: [email protected] Copyright © 2013 John Wiley & Sons, Ltd.

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There are several finite element head models in the literature that have investigated human head and brain response to blast [4–11]. These have generally been limited by coarse finite element meshes (>1 mm) [1, 4, 9, 11], or using tetrahedral element formulations [5, 10, 11] that may exhibit hydrostatic locking [12, 13], or the use of voxels [7] that do not accurately model tissue geometry and interfaces. Coarse elements or tetrahedral elements are unsuitable for blast models because they cannot accurately resolve wave phenomena and may give erroneous results. Recently, Zhu et al. presented 3D blast models of pig and rat heads with hexahedral elements of less than 1 mm in size [14, 15]. However, the pig model only included 1.22 million elements, compared to 1.98 million elements in our simple human head representation (Appendix A). In the case of the rat model (0.26 million elements), it is a much smaller overall volume and may require finer element discretization to accurately represent the structures in the head. Panzer et al. developed a plane-strain finite element blast model similar to Cronin et al. [16], although they only considered the transverse plane of the head and did not validate the model against experimental data [6]. It has been widely reported that viscoelasticity and the rate of loading play an important role in the brain response in blast scenarios [8]. However, the mechanical behavior of brain tissue in blast loading is not well understood because of the limited quantification of expected strain and strain rate values in the literature, and the large variation in published mechanical properties for this tissue. To address the limitations of existing models, 3D slice finite element models, in the sagittal and transverse planes of the head, were developed, while maintaining hexahedral elements of the order of 1 mm in size, which are needed to sufficiently resolve pressure wave effects [12]. These models were coupled to an air-blast model, validated against experimental test data and used to investigate the local tissue and global kinematic response of the head in the slice models exposed to blast loading in the context of primary blast injury. 2. BACKGROUND 2.1. Blast interaction with the head Blast overpressure is defined as the rapid rise in ambient pressure as a result of an explosive detonation, typically followed by an exponential decay in pressure. For this work, we assume the body is sufficiently far from the explosive so there is no interaction with the contact surface of the explosive. For conventional high explosives such as C4 or TNT, the typical positive pressure load durations are on the order of 2–10 ms, depending on the size of the explosive and proximity to the subject [17,18]. There are two distinct measures of blast overpressure: static pressure and dynamic pressure. Static pressure, also called incident or side-on pressure, is the pressure experienced by a particle within the blast flow and is often used as a reference in experimental testing. Dynamic pressure is related to the kinetic energy of the fluid or gas and interaction with a structure, which depends on the size, shape and compliance of the structure. When a pressure wave impinges on a surface, a portion of the wave is reflected and interacts with the remainder of the incoming wave, resulting in a greater net pressure experienced by the surface, often described as the reflected pressure [17]. Primary blast injury is defined as injury resulting from interaction of the blast pressure wave with the human body, disregarding secondary effects such as fragmentation and tertiary effects such as global translation and impact of the body. Previously, Cronin et al. showed that the primary blast interaction with the head occurs generally on the order of milliseconds, whereas accelerations due to global translation and falling occur on the order of seconds [16]. As such, the sagittal and transverse models, used to investigate primary effects, focus on short durations, on the order of milliseconds [19]. 2.2. Overview of experimental brain response data Because of the difficulty in obtaining experimental data of human brain response to blast loads, cadaver and animal test data must be used to validate the models. Intracranial pressure and head acceleration data have been reported for cadavers in high velocity blunt impact scenarios, originally intended for the automotive industry [20, 21]. Copyright © 2013 John Wiley & Sons, Ltd.

Int. J. Numer. Meth. Biomed. Engng. 2014; 30:470–489 DOI: 10.1002/cnm

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D. SINGH, D. S. CRONIN AND T. N. HALADUICK

More recently, Wayne State University conducted post mortem human specimen (PMHS) tests in shock tube blast load scenarios and measured intracranial pressure traces at various locations in the brain tissue [22]. There have also been numerous studies published in recent years looking at the intracranial pressure of live animal subjects in response to blast, both rodent [23–25] and porcine [26, 27]. Shridharani et al. reported peak intracranial pressures in porcine subjects to be 0.12–0.31 times the peak reflected pressures at the surface of the head [27]. Hardy et al. used high speed imaging techniques to map brain tissue motion relative to the skull in cadavers under blunt impact loads [28]. The deformation of the brain on live human volunteers has also been investigated in mild impact conditions, although the accelerations in these tests were significantly lower than those experienced in automotive impact or blast scenarios [29, 30]. Although there are some limitations due to geometry and/or experimental setups, these experimental studies provide sources of validation data over a wide range of load conditions for the sagittal and transverse head finite element models. However, the sagittal and transverse models were developed to investigate primary blast injury and are only applicable to short duration events. 2.3. Potential head injury thresholds for blast scenarios A significant challenge in the area of impact biomechanics is correlating measured tissue response to the potential for injury. Investigating brain injury provides additional challenges because the limited understanding of brain injury mechanisms especially in blast loading scenarios. Some recent experimental studies have correlated incident overpressure and duration with head injury using probability risk curves [31, 32]. However, the purpose of detailed finite element models is to predict response and the potential for injury at the kinematic or tissue level, such as head acceleration and tissue stresses and strains. A commonly used brain injury metric for both blast and blunt impacts is dynamic intracranial pressure, although a wide range of threshold values (66–234 kPa) has been reported in the literature [2, 33, 34]. Negative intracranial pressure has also been hypothesized as a potential injury mechanism, possibly by cavitation of the cerebrospinal fluid (CSF) [35]. CSF cavitation thresholds have largely been estimated based on the properties of water, which cavitates at negative pressures between 0.1 and 20 MPa, depending on the level of aeration [36]. A negative pressure threshold for CSF cavitation corresponding to 50% risk of injury was reported by Deck et al. to be 135 kPa [37]. Panzer et al. used a negative pressure cut-off value of 100 kPa in their plane-strain blast head model, corresponding to 1 atmosphere of negative pressure [6]. A negative pressure threshold of 1.5–3.5 MPa for soft tissue cavitation was reported by Coleman et al. [38]. First principal strain in the brain tissue, evaluated at a continuum level (i.e. not differentiating between white and gray matter), is another common brain injury metric, although the threshold values differ in the literature. Research on rats by Wayne State University concluded that a peak principal strain of 0.121 indicated axonal damage [39], and more recently, 0.30 correlated with brain contusion volume [40]. Kleiven proposed a principal strain of 0.21 for a 50% probability of concussion [33], and Deck et al. reported a threshold of 0.40 for severe diffuse axonal injury [37]. It should be noted that all of thresholds were developed for automotive crash-type impact scenarios. Another method of evaluating brain injury is to consider the overall head kinematics in terms of acceleration response. In general, the human head can withstand greater accelerations for shorter durations, but there is no consensus in terms of acceleration thresholds for very short durations relevant to blast. However, an automotive head injury criterion based on acceleration does exist and can be used as a benchmark to evaluate kinematics resulting from blast load. The Head Injury Criterion (HIC) is the most widely used automotive head injury prediction criterion. The HIC is calculated using a time integral of the total linear acceleration in g’s of the head over a specified duration in seconds (Equation 2.3). The integral duration, .t2 t1 /, is chosen such that the HIC value is maximized. For a 15 ms maximum calculation time window, the automotive industry uses a HIC tolerance limit of 700 [41]. HIC has been used in previous studies evaluating blast loads [42, 43], although it only considers resultant translational acceleration. Copyright © 2013 John Wiley & Sons, Ltd.



( HIC D max

1 .t2 t1 /

Z

)

2.5

t2

a.t/dt

473

.t2 t1 /

t1

Other head kinematics criteria have been proposed using rotational velocity and acceleration [44], or total power input to the head [45]. However these criteria have been found to produce results comparable to HIC for a wide range of blast load cases [16], and so only HIC was considered in this study. It must be emphasized that many of the existing criteria and thresholds have been developed for automotive-type impact scenarios and have not been verified for blast overpressure scenarios; however, the existing data and criteria provide an important starting point to investigate the potential for head injury from blast overpressure. 3. METHODS Head and brain tissue response from blast loading was investigated using an explicit finite element code (LS-DYNA v971, LSTC, Livermore, CA), which has been widely used in explosive detonation simulation and impact biomechanics. This study used 3D slice head models, in the sagittal and transverse planes (Figure 1), initially developed by Cronin et al. [16] and Lockhart [46]. The geometries for the head models were derived from the Visible Human Project male data set [47]. The slice models were composed of 3D solid hexahedral elements, which are recommended for computational accuracy in modeling wave phenomena and blast loads [48]. A comparison study (Appendix B) of the sagittal model using tetrahedral elements demonstrated that a tetrahedral mesh predicts intracranial pressures approximately 300% greater than hexahedral elements, emphasizing the importance of using hexahedral elements in blast simulations. The models were composed of solid Lagrangian elements embedded in an Eulerian air domain and included the relevant tissues (brain, skull, skin, muscle/soft tissue, CSF, vertebrae and vertebral discs). Because primary blast injury is by definition dominated by pressure wave dynamics, meaningful numerical models of such phenomena must have sufficient mesh resolution to resolve wave propagation accurately. An average element size of 1 mm was determined by Lockhart in a grid convergence study of the sagittal model, in agreement with previous studies [6, 46, 49]. Such a fine resolution requirement limits the computational feasibility of developing full 3D models of the head with necessary continuity between structures. Solid slice models allow for a fully coupled analysis with accurate wave propagation, while managing computational demand. To facilitate accurate wave propagation of pressure waves within the head models, nodes between adjacent tissue layers were merged, resulting in a continuous mesh. It has been noted that this could affect possible relative motion between adjacent tissues, particularly in the CSF where significant sliding motion may occur. However, as the strains observed in these models were much smaller than typical automotive cases and previous studies comparing contact interfaces demonstrated no significant difference in results [4], this boundary condition was found to be reasonable for the blast

Figure 1. Visible Human Project sagittal slice and head model (L), transverse slide and head model (R); (a) brain, (b) cerebrospinal fluid, (c) skull, (d) spinal cord, (e) muscle tissue, (f) skin, (g) vertebrae, (h) vertebral discs, (i) eyes (soft tissue) and (j) sinus (soft tissue). Copyright © 2013 John Wiley & Sons, Ltd.


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Figure 2. Lagrangian head model in Arbitrary Lagrange Eulerian (ALE) air mesh with inset.

Table I. Constitutive material properties for tissue materials. Tissue Skull/Vertebrae [16] Vertebral Discs [50] Skin [16] Muscle/Soft Tissue [51, 52] CSF [51] Brain/Spinal Cord [53]

Material model

Density (kg/m3 /

Elastic Elastic Elastic Hyperelastic

1561 1040 1200 1050

Fluid Linear Viscoelastic

1040 1050

Poisson’s ratio

Young’s mod. (Pa)

0.379 0.40 0.42

7.92e9 3.4e6 1.7e9

Bulk mod. (Pa)

2.2e9 2.2e9 2.2e9

scenarios considered. All nodes in the models were constrained from out-of-plane rotation or translation. Furthermore, the bottom layer of nodes at the neck of the sagittal model was fully constrained to capture rotational effects caused by the neck and torso interface. Otherwise, the models are free to rotate and translate in plane. These boundary conditions are suitable for the very short durations relevant to primary blast injury, which occur before significant motion of the head. The surrounding air was modeled using an Arbitrary Lagrange Eulerian (ALE) formulation resulting in a fully coupled analysis. The ALE air elements are suited to model the transmission of the blast wave through the air and the large deformations caused by interaction with the head. The size of the air elements adjacent to the head models was 1 mm (Figure 2), to facilitate accurate coupling between the Lagrangian and Eulerian components and ensure accurate prediction of the wave interaction. The air mesh was graded away from the head models to improve computational efficiency, with overall dimensions of the air model being 1.20 m 2.05 m to eliminate the effects of boundary reflections. Each tissue in the models was assigned relevant constitutive properties, based on the constitutive models used by Lockhart [46] (Table I). Because the tissue deformation is small over the duration of the response to blast, failure models were unnecessary for the structural components of the head, such as the skull. The brain tissue was modeled as a homogeneous material using a linear viscoelastic constitutive model, which has been previously deemed acceptable in comparison to experimental data [58]. Although recent studies have investigated directional aspects of the brain tissue [59, 60], the constitutive models used in this study were measured for larger samples of tissue and assumed isotropy; therefore, the tissue was modeled as continuous and isotropic. Regarding current or available brain tissue mechanical properties, there is a wide range of viscoelastic material constants reported in the literature (Table II), which were compared in this study. In cases where the literature reported different values for different regions of the brain, the average was taken. The total range of material constants considered in this study encompassed the differences in tissue regions reported by the authors, so in terms of evaluating the range of responses given by the various viscoelastic parameters, this averaging was deemed acceptable. Copyright © 2013 John Wiley & Sons, Ltd.



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Table II. Constitutive material properties for brain tissue. Literature source

G0 (Pa)

G1 (Pa)

B.s 1 /

Takhounts et al. [54] Zhu et al. [55] Zhang et al. [56] Ipek et al. [53]

1662 15900 44333 49000

928 3600 7333 16200

16.95 504.5 400 145

Table III. Viscous fluid material properties. Density (kg/m3 / Dynamic viscosity (Pas) Gruneisen EOS parameters [57]

1050 8.90e-4 C D 1483, S1 D 1.75, D 0.28

EOS, equation of state.

Figure 3. Schematic of blast scenario with slice model.

In addition to comparing the different viscoelastic models, the brain tissue was also modeled as a viscous fluid material with bulk properties similar to those of water (Table III). The response of such a material would give minimal resistance to dynamic shear and thus predicts maximum strains for a given load case. This effectively provided an upper bound on expected strains in the brain tissue under the blast load scenarios investigated. Three blast load cases were considered in this study, corresponding to cases for which experimental acceleration data exist from tests conducted by the Defence Research and Development Canada Valcartier [61]. The load cases were 5 kg of C4 high explosive at standoff distances of 3, 3.5 and 4 m, at 1.5 m height of burst, corresponding to peak incident pressures of 326, 230 and 170 kPa, respectively (Figure 3). The positive pressure phase durations for these blast load scenarios were on the order of 3 ms. For the charge size and standoffs considered in this study, the Mach stem triple Copyright © 2013 John Wiley & Sons, Ltd.


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point did not directly impinge on the head, as may be the case for larger standoffs [62], so no ground interaction was included in the models. To apply the blast load to the head models, the boundary ALE elements on the leading edge of the air domain (Figure 2) were given prescribed specific volume and temperature histories as a boundary condition. The Rankine–Hugoniot relations for air [63] were used to calculate the specific volume and temperature for each load case, from pressure wave curves extracted from LS-DYNA through the Conventional Weapons formulations. This prescribed boundary condition induced a pressure wave that propagated through the air mesh and interacted with the head models through a fluidstructure interaction coupling algorithm. Because the blast pressure wave is well-approximated as a planar wave, the bulk of the loading on the head will be translational, so rotational effects will be minimal. This has been verified using a multibody human model exposed to blast, including the mach stem effect [61, 62, 64]. This method of simulating blast loads has been used previously in the literature [3, 6, 16]. To investigate the applicability of using sagittal and transverse models to represent a 3D structure, a side study (Appendix A) was undertaken to compare the pressure response of a 3D ellipsoid with analogous sagittal and transverse slices of that ellipsoid, using the same ALE coupling method, blast load scenario and material properties described previously. It should be emphasized that the simplified ellipsoid model was not meant to accurately model the biomechanical response of the human head, only to compare with corresponding sagittal and transverse ellipse-shaped models to evaluate the applicability of using slice models to represent a 3D geometry. The findings of this 3D ellipsoid model study demonstrate that sagittal and transverse slice models of a simplified ellipsoid head blast model are able to predict frontal, temporal and parietal peak pressures. However, the slice models underpredict both positive and negative pressure magnitudes at the occipital side (back) of the ellipsoid due to the lack of 3D superposition of the pressure wave. It should be noted that the ellipsoid model assumes symmetry about the transverse plane and thereby neglects the neck and torso, which would reduce the superposition effect in an actual human head and lead to reduced pressure magnitudes. 4. RESULTS 4.1. Model validation Previously, Lockhart et al. [46] demonstrated that the acceleration versus time traces for the sagittal model accurately reproduced the measured head acceleration values for a physical test of a Hybrid III subjected to a 5 kg C4 charge at standoff distances of 3, 3.5 and 4 m. The predicted intracranial pressure of the transverse and sagittal models can also be compared to animal test data. A recent study measured intracranial pressure of live porcine specimens in blast [27]. The attenuation ratios, or the ratio of peak intracranial pressure to peak reflected pressure at the surface of the head, reported in that study ranged from 0.12 to 0.31 for the tested overpressures. Attenuation ratios in the sagittal and transverse models range from 0.35 to 0.44 for similar overpressure magnitudes, which is in reasonable agreement considering the inherent differences in structure between porcine and human heads. In particular, the porcine skull is much thicker than the human skull and would be expected to produce smaller attenuation ratios. In order to validate the sagittal and transverse model intracranial pressure response, the model response was compared to PMHS tests conducted by Bir [22]. The details and results of this validation study are included in Appendix C. The agreement between the model and experimental curves was quantified using cross-correlation software (CORA software, Partnership for Dummy Technology and Biomechanics, Ingolstadt, Germany) [65, 66].), with R2 values of 0.840, 0.680, 0.610 and 0.400 for frontal, temporal, parietal and occipital locations, respectively. The sagittal and transverse models show good agreement with the experimental data in the frontal, temporal and parietal regions of the brain tissue, particularly given the scatter in the data, which is typical of this type of testing. The models underpredict negative pressure and durations at the occipital region. This is in agreement with the findings of a 3D ellipsoid model study (Appendix A) and may be due to the lack of 3D pressure wave superposition effects at that location. Copyright © 2013 John Wiley & Sons, Ltd.



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Figure 4. (a) Peak linear acceleration and (b) HIC15 of models and experimental data.

Figure 5. Acceleration response of models compared to the Generator of Body Data (GEBOD) [47] for 3 m standoff.

4.2. Head kinematics The peak accelerations of the transverse and sagittal head models were compared to a simplified rigid body numerical model of a human called the Generator of Body Data (GEBOD), as well as to experimental data on a Hybrid III crash test dummy head exposed to actual blast loading [53]. The acceleration response for the slice models was measured at the node corresponding to the center of gravity of the head in each model. All acceleration data were filtered using a CFC1000 filter to match the experimental data, and the HIC15 values for each load case were calculated in LS-DYNA using the acceleration response curves. Application of this filter did not significantly affect the predicted HIC15 values. The transverse and sagittal models expectedly demonstrated decreasing peak accelerations and HIC15 values as standoff distance increased (Figure 4). The peak accelerations of the slice models and the GEBOD model were in good agreement with each other (Figure 5), although slightly overpredicted for the 4 m standoff in comparison to experimental data. The sagittal and transverse models are able to predict resultant head kinematics from the primary blast interaction because these events occur on the millisecond time scale, prior to bulk motion of the head. The HIC15 values for the numerical models were also in good agreement with each other and within the range of experimental data for the 3 m standoff, however, overpredicted for the 3.5 m and 4 m standoffs. 4.3. Pressure wave and head interaction Impingement of the overpressure wave on the head generates pressure waves in the underlying tissues. Pressure waves propagating in the brain tissue can be observed in both the sagittal and transverse models, demonstrating how stress waves can be transmitted through soft tissue pathways and into the brain (Figure 6). The waves propagate in the brain at 1560 m/s, consistent with Copyright © 2013 John Wiley & Sons, Ltd.


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Figure 6. Pressure histories demonstrating blast interaction with the head and tissues.

Figure 7. Maximum strains for constitutive parameters in (a) sagittal and (b) transverse models at 4 m standoff.

the acoustic wave speed for brain tissue in the literature [67]. The greatest intracranial pressures reported by both the sagittal and transverse models occurred on the anterior portion of the brain, during the primary impingement of the blast pressure wave. The primary pressure waves generally passed through the head in less than 600 s, while the wave duration was on the order of 3 ms. Skull flexure was observed in both models as a structural response to the blast. 4.4. Brain tissue property analysis The response of the brain tissue was investigated in terms of first principal strain and effective (equivalent) strain rate for the sagittal and transverse models using the different tissue properties available in the literature (Table II) and a viscous fluid model, to provide an upper bound on expected strains for the simulated blast load cases. Effective strain rate is an invariant quantity commonly used to express material rate of deformation for material mechanical data. In general, the different material models predicted maximum strains that increased in accordance with their shear modulus magnitudes (Figure 7, 4 m standoff). The most significant difference was for the fluid model, which predicted higher values of strain as expected. However, the maximum effective strain rate predicted in the brain tissue for the different constitutive parameters did not differ significantly (Figure 8). No significant difference in intracranial pressures was found for the varying constitutive parameters. 4.5. Brain tissue response The brain tissue response for both the sagittal and transverse models was investigated considering first principal strain, and positive and negative intracranial pressure. The linear viscoelastic constitutive parameters from Zhu et al. [55] were used for these simulations, providing a median strain Copyright © 2013 John Wiley & Sons, Ltd.



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Figure 8. Maximum strain rates for constitutive parameters in (a) sagittal and (b) transverse models at 4 m standoff.

Figure 9. First principal strain for (a) sagittal and (b) transverse models at standoff distances of 3, 3.5 and 4 m.

response (Figure 7) compared to other values in the literature. These data are presented in plots illustrating the volume fraction of the brain exposed to maximum values of pressure or strain for three blast scenarios. The maximum principal strains for the 4, 3.5 and 3 m standoff distances were 0.053, 0.054 and 0.087 for the sagittal model, and 0.035, 0.038 and 0.062 for the transverse model, respectively. However, most of the brain volume experienced smaller strains than these maximum values, with only approximately 10% of the volume experiencing higher strains (Figure 9). The locations of the maximum strains were near the brainstem in the sagittal model, and near the sinus cavity in the transverse model. Bayly et al. measured deformation in the brain during mild frontal and occipital head impacts and reported principal strains of 0.05–0.06 [29]. Although the impulse was not reported in the study, the peak accelerations in these experiments were in general three orders of magnitude lower in value and three orders of magnitude greater in duration than typical blast load scenarios. The automotive finite element model of Takhounts et al. reported a maximum principal strain of 0.347 with 135 g of peak linear acceleration [54]. Overall, the principal strains predicted by the models under blast conditions are relatively low compared to automotive models [37, 68]. The sagittal model reported maximum shear strains about 10% greater in magnitude than the principal strains. Conversely, the transverse model reported shear strains about 20% lower in magnitude than the principal strains. In general, the shear strains in both models exhibited similar trends to the principal strains with regard to standoff distance. The maximum effective strain rates predicted by the models ranged from 378 to 571 s1 for the sagittal model, and 226 to 425 s1 for the transverse model, depending on standoff distance. Strain rates of this order of magnitude are expected in blast load cases because of the extremely short load durations involved [69, 70]. Copyright © 2013 John Wiley & Sons, Ltd.


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Figure 10. Intracranial pressure for (a) sagittal and (b) transverse models.

Figure 11. Negative intracranial pressure for (a) sagittal and (b) transverse models.

The positive intracranial pressure response for both slice models demonstrated the expected trend of increasing pressure with decreasing standoff distance (Figure 10). The maximum positive intracranial pressure values for the models ranged from 273 to 578 kPa in the sagittal and 419 to 645 kPa in the transverse model. The negative intracranial pressure response of both models ranged from 211 to 410 kPa in the sagittal model and 365 to 760 kPa in the transverse model (Figure 11). The transverse model predicted higher values of both positive and negative pressure in the brain than the sagittal model. In general, the magnitudes of maximum positive pressure were comparable to the magnitudes of maximum negative pressure, both on the order of several atmospheres. Both models reported the largest values of positive pressure on the anterior brain tissue and the largest negative pressure on the posterior. 5. DISCUSSION AND CONCLUSIONS This study compared the head kinematics and tissue response of two finite element head models in the sagittal and transverse planes subjected to blast loads, in relation to injury metrics in the literature. The strain and strain rate response with different viscoelastic constitutive parameters for brain tissue was also investigated, including an idealized fluid brain material to provide an upper bound on expected strains in the brain tissue under the given load. In contrast to many blast head models in the literature, the models were validated against experimental data for both head kinematics and intracranial pressure. The peak accelerations of the models were in good agreement with each other as well the numerical GEBOD model; however, they were slightly overpredicted in some cases in comparison with experimental data. This is attributed to the large amount of scatter in the experimental data, often associated with blast testing. Both slice models exceeded the HIC15 threshold of 700 for the 3 m Copyright © 2013 John Wiley & Sons, Ltd.



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standoff, only the transverse model exceeded it for the 3.5 m standoff and neither model exceeded it for the 4 m standoff. Although HIC provides a useful benchmark for evaluating model response, it should be noted that the HIC was developed in the automotive industry for load durations longer than those applicable to blast. The slice models reported principal strains in the brain between 0.035 and 0.087 for the blast load cases considered. These are lower than those seen in typical automotive crash scenarios, which typically predict principal strains of 0.20 and greater [68]. However the strain rates in the brain tissue predicted by the slice models ranged from 226 to 571 s1 , significantly greater than rates observed in automotive models, which generally range from 10 to 100 s1 [37]. The principal strain response of the models decreased as the shear modulus of the brain constitutive models increased; however, the predicted effective strain rate was not affected significantly for the range of loading considered in this study. The fluid material model predicted principal strains greater than any viscoelastic model. The models reported relatively high intracranial pressures (273–578 kPa in the sagittal and 419– 645 kPa in the transverse) in comparison with existing injury metrics in the literature, which range from 66 to 234 kPa, although the applicability of these injury metrics to blast loading is unclear. The maximum negative pressures predicted by the models were also on the order of several atmospheres of negative pressure and are likely underpredicted because of the lack of 3D pressure wave effects. The proposed or measured thresholds for negative pressure by means of cavitation vary widely in the literature: from 100 kPa to 20 MPa for water, so the potential for negative pressure as an injury mechanism remains a possibility. Both models reported the greatest positive pressures on the anterior of the brain and the greatest negative pressures on the posterior, suggesting the possibility of a coup, contre-coup injury mechanism. A limitation of these models is that 3D wave effects could not be predicted, which was shown to affect the predictions at the posterior of the models for frontal blast exposure, where the pressure was underpredicted. Another limitation is that these models are only appropriate for primary blast injury, which occurs in the initial wave transmission and reflection through the head, on the order of milliseconds. Beyond this time regime, the head may undergo gross macroscopic motion, depending on the blast scenario. Importantly, these models have allowed us to associate increasing tissue response, with increased blast load severity, and to quantify expected strains and strain rates experienced in brain tissue. This study clearly demonstrates that brain tissue response from typical blast loading produces strains on the order of 1 magnitude lower and strain rates on the order of 1 magnitude higher than typical automotive scenarios. Based on these results and the evaluation of common injury metrics, the use of a single strain value was not consistent between automotive and blast scenarios, demonstrating that injury tolerance thresholds may depend on deformation rate as well. Metrics based on intracranial pressure were more consistent with existing thresholds from the automotive community, and because this measure inherently includes the severity of loading, it may provide promise as an injury metric. Future material characterization should focus on measuring tissue properties in these regimes and on improved characterization of cavitation response. Although the relevance of existing injury criteria to blast is unclear, these models have demonstrated that all response metrics follow the trend of increasing response with blast severity, which can be used to evaluate protection and mitigation strategies in future analysis.

APPENDIX A: THREE-DIMENSIONAL ELLIPSOID STUDY In order to investigate the validity of using the sagittal and transverse models to represent a 3D head, a study was undertaken using a simplified 3D ellipsoid shape (Figure A1). This ellipsoid model approximated the general shape and dimensions of the head and brain and allowed for investigation into 3D wave effects, while being relatively simple to develop. The purpose of this side study was to compare the intracranial pressure response of the 3D ellipsoid with sagittal and transverse slice models of the ellipsoid to determine the validity of the slice model results. Copyright © 2013 John Wiley & Sons, Ltd.


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Figure A1. Three-dimensional ellipsoid model.

Figure A2. Ellipsoid model embedded in air mesh, with inset.

Methods The 3D ellipsoid model consisted of a simplified brain, a CSF layer and a skull layer (Figure A1). The dimensions of the quarter ellipsoid brain were 0.0605 0.0654 0.152 m, defined to correspond to the general proportions of the human brain. A 2 mm CSF layer and a 5 mm skull layer surrounded the ellipsoid brain. These dimensions and geometry were comparable to the human head sagittal and transverse models in our study. The ellipsoid model was meshed with solid Lagrangian hexahedral elements, with an average element size of 1 mm, consistent with the element size on the detailed anatomical sagittal and transverse head models used in the main body of the manuscript. Because of the symmetrical nature of the ellipsoid shape, a quarter model was used to minimize computational demand, whereas a 1/2 symmetry model would be required for a 3D human head. The 3D quarter ellipsoid model consisted of 1 977 664 elements. The same material properties for brain, CSF and skull tissue were used as described in the main body of the paper. The ellipsoid model was embedded into a rectangular Eulerian air mesh using the same ALE coupling method as described in the main body of the paper, resulting in a fully coupled analysis (Figure A2). The element size in the air mesh was 1 mm in the vicinity of the ellipsoid model to maintain accurate coupling, and larger near the boundaries to reduce computational demand. The dimensions of the air mesh were 0.5 0.5 0.8 m, sized to prevent boundary reflections from interfering with the models. The air mesh consisted of a total of 5 507 600 elements. To apply the blast load to the 3D ellipsoid model, the same method was used as described in the main body of the paper, where temperature and specific volume histories were prescribed on the leading edge of the air mesh, resulting in a blast wave propagating through the air and impinging on the head model. Using the geometry of the 3D ellipsoid model, sagittal and transverse slices were created, analogous to the detailed sagittal and transverse models used in the Copyright © 2013 John Wiley & Sons, Ltd.



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paper (Figure A3). All three models (the 3D ellipsoid, the sagittal slice and the transverse slice) were exposed to the same blast wave simulating a 5 kg charge of C4 at 4 m standoff. The model took 120 h to run on our fastest machine (Intel i7-990X with 12 cores). Results Peak intracranial pressures for the 3D ellipsoid model and the sagittal and transverse slices of the ellipsoid were compared for various locations in the models (Figure A4). The ellipsoid slice models reported slightly greater pressures (10–13%) at the frontal location, while the parietal and temporal locations were in good agreement (>5% difference). The most significant difference observed in this comparison study was at the occipital location, on the posterior side of the brain, where the ellipsoid slice models underpredicted the peak positive and negative ICP magnitudes. This is due to pressure wave reflection and superposition within the skull. In the 3D ellipsoid model, the superposition of the pressure wave is significant because the pressure travels along all planes of the 3D structure. In the slice models, the wave superposition only exists in one plane, so the resultant pressures at the occipital end are smaller. It should be noted that the ellipsoid model may overemphasize this effect because the geometry is essentially focusing the waves, and the more complicated shape of the human skull will not have as significant of an effect.

Figure A3. Illustration of ellipsoid sagittal and transverse slices.

Figure A4. Peak (a) positive and (b) negative pressures for three-dimensional ellipsoid model and sagittal and transverse slices, at various locations. Copyright © 2013 John Wiley & Sons, Ltd.


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Conclusions The findings of this 3D ellipsoid model study suggest that sagittal and transverse slice models of a simplified ellipsoid head blast model can predict frontal and parietal peak pressures. However, the slice models underpredict both positive and negative pressure magnitudes at the occipital side of the ellipsoid because of the lack of 3D superposition of the pressure wave. It should be noted that the ellipsoid model assumes symmetry about the transverse plane and thereby neglects the neck and torso, which would disrupt the pressure wave transmission in an actual human head and lead to reduced pressure magnitudes. APPENDIX B: COMPARISON OF HEXAHEDRAL AND TETRAHEDRAL ELEMENT TYPES To demonstrate the effect of using single integration point tetrahedral elements for a blast problem, the sagittal head model was meshed with tetrahedral elements and the predicted intracranial pressures were compared to the original hexahedral element mesh. Four-noded constant stress tetrahedral elements were generated using the geometry of the sagittal model. The tetrahedral elements had an average side length of 1 mm, consistent with the hexahedral elements (Figure B1). Both the hexahedral and tetrahedral meshes were run for the 5 kg of C4 at 4 m standoff blast load case, and peak pressures at the frontal, parietal and occipital locations compared (Figure B2). The tetrahedral mesh predicted peak intracranial pressures about 300% greater than the hexahedral elements for all locations. Furthermore, the tetrahedral mesh demonstrated significant local variability in elemental pressures, which was not present in the hexahedral mesh. For example at the frontal location, peak pressures varied from 230 to 470 kPa for directly adjacent elements (Figure B3), demonstrating typical hydrostatic locking that may occur when using tetrahedral elements for this type of problem. The high local variability and significantly greater intracranial pressures predicted by the tetrahedral mesh suggests that hydrostatic locking is a major issue that affects tetrahedral elements in

Figure B1. Close-up of (a) hexahedral and (b) tetrahedral meshes.

Figure B2. Comparison of peak positive pressures between hexahedral and tetrahedral meshes at various locations. Copyright © 2013 John Wiley & Sons, Ltd.



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Figure B3. Elemental pressure histories for tetrahedral elements at frontal location, demonstrating large variability in peak pressures.

blast simulations, which can lead to erroneous results. This underscores the importance of using hexahedral elements in finite element blast models. APPENDIX C: INTRACRANIAL PRESSURE VALIDATION STUDY The sagittal and transverse models were compared to post mortem human subject (PMHS) tests conducted by Bir [21]. These tests used a shock tube to simulate a blast pressure wave and exposed a cadaveric human head to the simulated blast. Optical pressure sensors were positioned in the brain tissue at the frontal, parietal, temporal and occipital lobes of the brain, and recorded intracranial pressure (ICP) traces (Figure C1). The experiments used blast overpressures of 71, 76 and 104 kPa, with positive phase durations of 7.5, 7.4 and 7.0 ms, respectively. These blast conditions were replicated in the ALE model from the current study and applied to the sagittal and transverse models using a prescribed specific volume and temperature boundary condition. The pressure histories of elements at locations in the head model corresponding to the locations referenced in the study were investigated. Although the study was not specific regarding the location, the variation in the peak pressures of surrounding elements was less than 5%, and the element closest to the location described in the experimental study was used. Also, the orientation of the PMHS relative to the incident blast wave may have been slightly different than the sagittal and transverse models that assume a horizontal Frankfurt plane, which could account for some of the differences. The ICP histories of the models were compared to the experimental measurements for each location (Figure C2).

Figure C1. Locations of frontal (black), parietal (blue), occipital (brown) and temporal (red) intracranial pressure measurements. Copyright © 2013 John Wiley & Sons, Ltd.


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Figure C2. Comparison of intracranial pressures of sagittal and transverse models with experimental data [21] for various locations at 71, 76 and 104 kPa blast overpressures.

Frontal and occipital pressures were extracted from both the sagittal and transverse models, parietal pressure was extracted from the sagittal and temporal pressure was extracted from the transverse model. It should be noted that the transverse model geometry corresponds to a slice at the level of the eyes, whereas the experimental measurements of ICP at the frontal and occipital locations are offset from this plane (Figure C1, left image). The experimental curves were compared to the model response quantitatively using crosscorrelation software (CORA), which outputs a determination coefficient (R2 / value that quantifies the model fit. CORA can also use experimental response corridors to evaluate correlation, but this mode of comparison was not possible because of the lack of repeat experimental data necessary to construct response corridors. The results of the CORA analysis are summarized in Table C1. In Table C1, the values shown are the R2 values when comparing the model predictions to each individual experimental result. In some cases, there were two experimental results for a particular load case, and the model prediction was compared to each individual test separately. The overall correlation for the frontal cases (R2 = 0.840) was very good, especially given the limited number of tests and the scatter in the data, although peak pressures were slightly under predicted (by 5%, 14% and 30% for the 71, 76 and 104 kPa overpressures, respectively). The pressure Copyright © 2013 John Wiley & Sons, Ltd.



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Table C1. Cross-correlation comparison of sagittal and transverse models to experiments (Bir 2011). Blast insult Low Mid High Mean

Front sagittal

Front transverse

Temporal

Parietal

Occipital sagittal

0.855 0.758 0.890 0.810 0.824

0.717 0.789 0.919 0.945 0.892 0.840

0.536 0.670 0.710 0.741 0.742 0.680

0.677 0.438 0.718 0.450 0.769 0.610

0.448 – 0.530 – 0.266

Occipital transverse 0.434 – 0.453 – 0.270 0.400

Mean 0.632 0.717 0.627 0.633

response at the temporal location (R2 = 0.680) generally followed the experimental curves for all three load cases. At the parietal location (R2 = 0.610), the sagittal model predicts similar peak pressures to the experimental data, although the durations were overpredicted. At the occipital location (R2 = 0.400), the negative pressure and duration were under predicted, as expected because of the under-estimation of the 3D focusing effect demonstrated by the ellipsoid model (Appendix A). It should be emphasized that a good estimate of variability in the experiments was not available; however, in cases where two experimental results were available for the same load case, the results were compared using the cross-correlation method to investigate the consistency of the experimental data. Overall, the average R2 between repeat experiments for all of the data was 0.595, demonstrating that the variability between similar experiments was comparable to the temporal and parietal model R2 values. Overall, the sagittal and transverse models predict pressures in agreement with the experimental data for the frontal, temporal and parietal regions. The occipital region demonstrated the most significant variation from the experimental data. This is acknowledged as a limitation of the sagittal and transverse slice models; as 3D wave superposition effects at the occipital region are not fully included in the models, negative pressures at the occipital region are underpredicted. ACKNOWLEDGEMENTS

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