ROLE OF ROTATIONAL ACCELERATION AND DECELERATION PULSES ON BRAIN STRAINS IN LATERAL IMPACT

ROLE OF ROTATIONAL ACCELERATION AND DECELERATION PULSES ON BRAIN STRAINS IN LATERAL IMPACT ABSTRACT Jianrong Li, Jiangyue Zhang, Narayan Yoganandan, Frank A. Pintar, Thomas A. Gennarelli Department of Neurosurgery, Medical College of Wisconsin, VA Medical Center, Milwaukee, WI USA The objective of the study was to determine the role of acceleration-deceleration pulses on brain strains in lateral impact. A coronal plane finite element model was developed and validated with experimental temporal motion and strain data from literature. Parametric studies were conducted by applying acceleration, deceleration, or combined acceleration-deceleration pulses with varying separating time intervals. Temporal principal strains were obtained at the corpus callosum, base of postcentral sulcus, and cerebral cortex of the parietal lobe regions. Results indicated region- and pulse-specific responses to angular accelerations and separating time intervals. Keywords: brain, finite element method, accelerations, diffuse brain injury TRAUMATIC BRAIN INJURY is a leading cause of disability and fatality in the United States. Approximately 1.4 million traumatic brain injury cases occur annually (Langlois et al., 24). Life time costs of TBI was $6 billion in 2, including direct medical and indirect costs such as lost productivity (Finkelstein et al., 26). Motor vehicle crashes are a primary source for these injuries (Gennarelli and Meaney 1996). Diffuse brain injury is one of the most severe types of TBI with high fatality and long term disability. Laboratory studies have been conducted to investigate injury mechanisms and establish diffuse brain injury thresholds. These models have used animals and physical models to investigate injury biomechanics (Gennarelli et al., 1982; Margulies and Thibault 1992; Bradshaw et al., 21). Physical models have used silicone gel to represent the human brain tissue. These models have used rotational acceleration as the input. is commonly associated biomechanical injury metric for injury quantification in these experimental literatures. Due to the limitations of the loading apparatus used in these experiments, the intended acceleration pulses are often accompanied by a deceleration pulse with short or long separating time intervals (Ommaya et al., 1966; Abel et al., 1978; Thibault et al., 1987; Margulies et al., 199; Bradshaw et al., 21; Gutierrez et al., 21). Peak decelerations have exceeded peak accelerations depending on the apparatus used (Ommaya et al., 1966; Thibault et al., 1987; Margulies et al., 199). In addition, the separation time between the acceleration and deceleration pulses ranged from zero to 1 ms, in the cited studies. Experimentally, it is difficult to precisely determine the role of the acceleration-deceleration pulse and separating time interval in injury production and quantification. The objective of the present study is, therefore, to delineate the roles of these parameters on injury metrics in lateral impacts using computational modeling. METHODS The anatomy and geometry for the head model is extracted from a experimental study (Bradshaw et al., 21). The two-dimensional physical model consisted of a cylindrical aluminium skull, aluminium falx, cerebral spinal fluid modeled by liquid paraffin, and cerebrum modeled by silicone gel (Figure 1a). The skull was 192 mm in internal diameter, the falx was 8 mm wide and 6 mm deep, and the cerebral spinal fluid layer was a 3/4 circle with thickness of 2.5 mm. The skull was IRCOBI Conference - Maastricht (The Netherlands) - September 27 173

rotated about the center of geometry. The angular acceleration consisted of two pulses: acceleration pulse, 4.5 ms, 7.8 krad/s/s; and deceleration pulse, 2 ms, 1.4 krad/s/s, separated by 1 ms separation time. The change in angular velocity of the deceleration pulse was equal to the acceleration pulse. o Figure 1: Finite element model. structures and locations used to extract the stress analysis output, and mesh. The finite element model, shown in figure 1b, is meshed by a preprocessor (MSC Inc., Santa Ana, CA), containing 465 elements and 4595 nodes. A nonlinear explicit finite element software ABAQUS/Explicit (Version 6.5, HKS Inc., Providence, RI) is used for the stress analysis. Material properties are obtained from literatures (Meyers and Chawla 1984; Bradshaw et al., 21). The aluminum skull and falx are assumed linear elastic: Young s modulus 7.3 GPa, Poisson s ratio.345, and density 2,7 kg/m 3 (Meyers and Chawla 1984). Both liquid paraffin and silicone gel are considered nearly incompressible. A hydrodynamic material model, governed by the Mie-Grüneisen equation of state in linear Hugoniot form, is used for the liquid paraffin. A linear viscoelastic material model is adopted for the silicone gel. Material properties of these two constituents are obtained from literature (Bradshaw et al., 21). The outer nodes of the skull are rotated about the center of geometry simulating the experiment. The right-handed rectangular Cartesian axes of reference OX 1 X 2 are defined with the origin at the rotation center of the model. These axes rotated with the model. To determine the role of the acceleration-deceleration pulse and separating time interval, four grouped scenarios are considered. The simulation matrix is shown in table 1. Briefly, groups 1 and 2 had only acceleration or deceleration. Groups 3 and 4 had both acceleration and deceleration pulses with separation times ranging from zero to 25 ms. Simulations are run in steps of 5 ms. Typical loading inputs for group 1, 2, 3 and 4 simulations are shown in figure 2. Motions and strains are obtained at the corpus callosum, base of postcentral sulcus, and cerebral cortex of the parietal lobe, shown in figure 1a. To further evaluate specific regional behaviors within the brain, the cerebrum is divided into seventeen regions (Figure 3). Peak values of average maximum principal strains in each region are determined. 174 IRCOBI Conference - Maastricht (The Netherlands) - September 27

Table 1: Simulation matrix. Group Pulse type Separating time interval (ms) 1 Acceleration pulse only None 2 Deceleration pulse only None 3 Acceleration pulse followed by deceleration pulse, 5, 1, 15, 2, 25 4 Deceleration pulse followed by acceleration pulse, 5, 1, 15, 2, 25 Angular acceleration (Krad/s/s) 1 8 6 4 2 5 1 15 2 Angular acceleration (Krad/s/s) 1 8 6 4 2 5 1 15 2 Angular acceleration Angular acceleration Time Time -1-1 (c) (d) Figure 2: Inputs used in group1, 2, 3, and 4 simulations: group 1, group 2, (c) group 3 and (d) group 4. See table 1 for details. Figure 3: Regions identified to compute the principal strains. IRCOBI Conference - Maastricht (The Netherlands) - September 27 175

RESULTS The finite element model is first validated against experimental temporal motion and strain data in the acceleration phase with a time period of 4 ms (as shown in figure 2a). The time-histories of displacements along X1 and X2 directions and maximum principal strain outputs from the finite element model are shown in figures 4a-c. Displacements match closely with experimental data (Figures 4a, 4b). The computed maximum principal strains predicted by the computer model agree well with the experimental data up to the development of peak strains (Figure 4c). 4 4 3 3 Displacement (mm) 2 1-1 Displacement (mm) 2 1-1 -2-2 -3 1 2 3 4-3 1 2 3 4 1.2 1.8.6.4.2 -.2 -.4 1 2 3 4 (c) Figure 4: Time-histories of displacements and maximum principal strains from the finite element model (lines) and experimental data (discrete symbols) at the corpus callosum (cc), base of postcentral sulcus (bps), and cerebral cortex of parietal lobe (cpl). Figures 4a and 4b correspond to displacements along X1 and X2 directions, and figure 4c corresponds to the maximum principal strain. Time-histories of maximum principal strains at the three regions in group 1 and 2 simulations are shown in Figures 5a-c. Table 2 includes strain data. Temporal maximum principal strains at all regions in group 2 simulation show delayed responses compared to group 1 simulation. Peak maximum principal strain at the corpus callosum (.42) in group 2 simulation is smaller than group 1 (.48) simulation (Table 2). In contrast, peak maximum principal strains at the base of postcentral sulcus and cerebral cortex of the parietal lobe in group 2 simulation are almost equal to group 1. Figure 6 shows peak values of region average maximum principal strains from group 1 and 2 176 IRCOBI Conference - Maastricht (The Netherlands) - September 27

simulations. In all regions, peak values from group 1 simulation are slightly greater than group 2 simulation. The largest difference occurred in the central brain and close to the falx, region 7..6.5 cc.6.5 bps.4.4.3.3.2.2.1.1 2 4 6 8 1 2 4 6 8 1.6.5 cpl.4.3.2.1 2 4 6 8 1 (c) Figure 5: Time-histories of maximum principal strains in group 1 and 2 simulations in the corpus callosum, base of postcentral sulcus, and cerebral cortex of the parietal lobe (c). outputs in group 1 simulation are shown by solid, and in group 2, are shown by dashed curves. Table 2. Peak maximum principal strains in group 1 and 2 simulations. Group Peak maximum principal strain at: corpus callosum base of postcentral sulcus cerebral cortex of the parietal lobe 1.48.4.27 2.42.39.26 IRCOBI Conference - Maastricht (The Netherlands) - September 27 177

.5 Group 1 Group 2.4.3.2.1 1 2 3 4 5 6 7 8 9 1 11 12 13 14 15 16 17 Region Figure 6: Peak region average maximum principal strains in group 1 and 2 simulations. Time histories of maximum principal strains at the corpus callosum, base of postcentral sulcus, and cerebral cortex of the parietal lobe in group 3 simulations for separating time intervals of, 1, 2 ms are shown in figures 7a-c. Compared to group 1 simulation, temporal maximum principal strains in group 3 simulations present two main peaks. The first peaks at the base of postcentral sulcus and cerebral cortex of the parietal lobe are lower in group 3 than group 1 simulation (Figure 7b and 7c). The first peaks increase with increasing separation times, reaching values close to group 1 simulation (Figure 7b and c). In contrast, the first peak strains in the corpus callosum region do not change significantly with separating time intervals (Figure 7a). magnitudes of the second peaks are smaller than the first ones, except at 2 ms time interval, the second peak at cerebral cortex of the parietal lobe is larger than the first one. Figures 8a and 8b illustrate variations in the magnitudes of the two peaks with increasing separating time intervals. Figure 9 shows peak region average maximum principal strains from group 1 and group 3 at zero and 2 ms separating time intervals. In all cases, region 7 sustains the highest strains, and regions 8 and 12 sustain the least strains. For group 3 with zero separation time, peak strains are always smaller than group 1. But the difference between group 1 and group 3 are small in regions 5, 6, and 7, surrounding the corpus callosum. However, strains in the peripheral regions from group 3 are considerably smaller than group 1. For group 3 with 2 ms separation, strains are approximately the same as group 1. Results of group 4 simulations are similar to group 3. Temporal maximum principal strains also present with two main peaks. Figures 1a and b show peak maximum principal strains at the three regions with increasing separation time. The first peaks of maximum principal strains are slightly smaller than group 3 simulations. The second peaks are close to group 3 simulations. 178 IRCOBI Conference - Maastricht (The Netherlands) - September 27

.6.6.5 Group 1 ms 1 ms 2 ms.5 Group 1 ms 1 ms 2 ms.4.4.3.3.2.2.1.1 2 4 6 8 1 2 4 6 8 1.6 Group 1 ms.5 1 ms 3 ms.4.3.2.1 2 4 6 8 1 (c) Figure 7: Time-histories of maximum principal strains at the corpus callosum, base of postcentral sulcus, and cerebral cortex of the parietal lobe (c) for group 1 (solid line) and group 3 simulations (line with symbols)..6.6.5.5.4.3.2.1 5 1 15 2 25 Separating time interval (ms) cc bps cpl.4.3.2.1 5 1 15 2 25 Separating time interval (ms) Figure 8: Peak maximum principal strains at the corpus callosum (cc), base of postcentral sulcus (bps), cerebral cortex of the parietal lobe (cpl) in group 3 simulations: the first peak; the second peak. cc bps cpl IRCOBI Conference - Maastricht (The Netherlands) - September 27 179

.5 Group 1 ms 2 ms.4.3.2.1 1 2 3 4 5 6 7 8 9 1 11 12 13 14 15 16 17 Region Figure 9: Peak region average maximum principal strains from group 1 and group 3 simulations with separating time intervals of and 2 ms..6.6.5.5.4.3.2.1 5 1 15 2 25 Separating time interval (ms) cc bps cpl.4.3.2.1 5 1 15 2 25 Separating time interval (ms) Figure 1: Peak maximum principal strains at the corpus callosum (cc), base of postcentral sulcus (bps), cerebral cortex of the parietal lobe (cpl) in group 4 simulations: first peak; second peak. cc bps cpl DISCUSSION As indicated briefly in the Introduction, acceleration profiles applied in experiments often consisted of both acceleration and deceleration pulses with varying separating time intervals, although the shape and pulse duration differed between studies. The dual pulse is due to variations in the design of the loading apparatus. For example, tests conducted at the University of Pennsylvania used a HYGE TM accelerating system which produced a lower peak acceleration pulse followed by a higher peak deceleration pulse with no separation (Thibault et al., 1987). Physical model experiments using a pendulum apparatus have produced a high acceleration pulse accompanied with a low deceleration pulse and a long separation time (Bradshaw et al., 21). Because the two pulses are coupled, difficulties exist in precisely determining the individual roles of the acceleration and deceleration pulses. This has forced investigators to provide rationale(s) for the metric correlating the injury based on certain mechanics assumptions or clinical observations regarding specific injury locations and anatomical considerations (Gennarelli et al., 1982; Oka et al., 1985). Thibault et al. suggested that the 18 IRCOBI Conference - Maastricht (The Netherlands) - September 27

experimentally-induced injuries were due to the deceleration pulse (Thibault et al., 1987). This was justified by mathematical analyses (Cheng et al., 199). Another analysis suggested acceleration pulse to be the biomechanical metric for diffuse brain trauma (Lee et al., 1987). Because longitudinal evaluations or histopathological assessments are done subsequent to a combined accelerationdeceleration loading and euthanasia, it is difficult to determine the specific rotational acceleration pulse responsible for the observed brain injury. In contrast, in the present preliminary study, a finite element modeling approach is used, as this technique has the unique ability to accurately determine injury metrics as a function of the entire pulse, temporal acceleration or deceleration, albeit the actual documentation of injury cannot be made with this methodology. In order to demonstrate the technique, a parametric approach is used, and in addition, a simple idealized two-dimensional model is adopted fully recognizing that the human brain is complex, three-dimensional, and housed in the relatively rigid calvarium. To be congruent with the literature, strain is chosen as the biomechanical metric to delineate the role of the two pulses and the separating time. Computed displacements and strains agreed very well with experimental results data before the variables reached peak values. However, deviations beyond the attainment of peak values may be due to brain viscoelasticity. A linear viscoelastic Maxwell model was adopted for the silicone gel. Although parameters for the Maxwell model were deduced from experimental data (Bradshaw et al., 21), differences between the fitted Maxwell model and the actual material behavior from experiments may have contributed to the post-peak discrepancy. The present analysis was based on a two-dimensional finite element model extracted from a physical model with simplified geometry and anatomy and used surrogate materials. This is a first step in the investigation of strain distributions using an in vivo human brain using the finite element method. Further studies are, therefore, necessary to account for the effects of complex three-dimensional anatomy and more realistic brain tissue properties on strain distribution to better understand the role of acceleration and deceleration pulses on TBI. Acknowledging that the two pulses had same change in angular velocity and the acceleration pulse is short and deceleration pulse is relatively long (4.5 versus 2 ms), the magnitude of acceleration appeared to slightly affect the central brain strain but not the peripheral brain strain, indicating the role of the peak angular acceleration to marginally affect tissues in the central region. This finding may suggest an elevated role for the angular velocity parameter as a potential injury metric. s under combined acceleration-deceleration pulse depend on the separating time interval. In effect, the structure sustains two impacts under the combined pulse, shown in figures 7ac. The unloading role of the second pulse, deceleration or acceleration corresponding to group 3 or 4, is to reduce the strain field induced by the first pulse. s in central regions caused by the first pulse seem to be affected less by the unloading effect of the second pulse (Figures 7a and 9). In contrast, strains in the peripheral regions due to the first pulse are greatly reduced by the second pulse at short separating time interval (Figures 7a, 7b, and 9). However, the first peak strains in the peripheral regions increase with increasing separation time intervals. The first peak strains reach magnitudes close to the maximum value under single acceleration pulse at the greatest separating time interval (Figure 7b and 7c). In group 1, the duration of acceleration is 4.5 ms, however, peak strains at the corpus callosum, base of the postcentral sulcus, and cerebral cortex of the parietal lobe occur at about 11, 34 and 32 ms, respectively, which are much delayed than the input acceleration pulse duration (Figures 7a-c). The delay between the mechanical response and loading varies with the anatomical location. This may be attributed to the viscous nature of the brain material. If the separating time interval is smaller than the delay between mechanical response and loading, brain strains are reduced. Otherwise, the second pulse would not affect strains caused by the first pulse. Compared to strains produced by a single pulse, strains from the second pulse in a combined loading with short separation times are small. Because of residual strains from the first pulse, the second peak strains are generally lower than the first peak (Figure 7a-c). s from the second pulse increase with increasing separation times (Figures 8b and 1b). These findings indicate that brain strains are region-, and pulse-specific. IRCOBI Conference - Maastricht (The Netherlands) - September 27 181

CONCLUSIONS At a specific change in angular velocity, peak strains are slightly greater at the corpus callosum region at higher peak acceleration (groups 1 and 2). s in the peripheral regions do not change with acceleration magnitude, indicating insensitivity with change in rotational acceleration. Combined loading (groups 3 and 4) produced peak strains generally lower than single rotational acceleration input (groups 1 and 2). Using pulse with greater magnitude as a potential injury metric underestimates brain strains in all regions. The role of each pulse on brain strain is such that increasing separating times increases peak strains in all regions. However, the increase is more pronounced at the peripheral regions than at the corpus callosum. At the greatest separating time, peak strains reach values close to peak strains produced by a single pulse. Therefore, experiments with longer acceleration/deceleration separation time can be treated as two independent loadings and the resulting injury may be attributed to the initial pulse. Thus, the brain demonstrates region- and pulse-specific responses under angular accelerations. Additional studies are needed to reinforce these conclusions as the present results are based on an idealized model simulating a specific scenario. ACKNOWEDGEMENTS This research was supported by VA Medical research. REFERENCES Abel, J. M., Gennarelli, T. A. and Segawa, H., 1978. Incidence and severity of cerebral concussion in the Rhesus monkey following sagittal plane angular acceleration. 22nd Stapp Car Crash Conference: 35-53. Bradshaw, D. R., Ivarsson, J., Morfey, C. L. and Viano, D. C., 21. Simulation of acute subdural hematoma and diffuse axonal injury in coronal head impact. J Biomech 34(1): 85-94. Cheng, L. E., Rifai, S., Khatua, T. and Piziali, R. L., 199. Finite element analysis of diffuse axonal injury. SAE International Congress and Exposition. Finkelstein, E., Corso, P., Miller, T. and associates. 26. The incidence and economic burden of Injuries in the United States. New York (NY): Oxford University Press. Gennarelli, T., Thibault, L., Adams, J., Graham DI, T., hompson, C. and Marcincin, R., 1982. Diffuse axonal injury and traumatic coma in the primate. Ann Neurol 12(6): 564-574. Gennarelli, T. A. and Meaney, D. F. Mechanisms of primary head injury. Neurosurgery. R. Wilkins and S. Rengachary. New York, McGraw Hill. 2: (1996) 2611-2621. Gutierrez, E., Huang, Y., Haglid, K., Bao, F., Hansson, H. A., Hamberger, A. and Viano, D., 21. A new model for diffuse brain injury by rotational acceleration: I model, gross appearance, and astrocytosis. J Neurotrauma 18(3): 247-57. Langlois, J. A., Rutland-Brown, W. and Thomas, K. E., 24. Traumatic brain injury in the United States: emergency department visits, hospitalizations, and deaths. Atlanta (GA): Department of Health and Human Services (US), Centers for Disease Control, and Prevention, National Center for Injury Prevention and Control 24. Lee, M. C., Melvin, J. W. and Ueno, K., 1987. Finite element analysis of traumatic subdural hematoma. 31st Stapp Car Crash Conference: 67-77. Margulies, S. S. and Thibault, L., 1992. A proposed tolerance criterion for diffuse axonal injury in man. J, Biomechanics 25: 917-923. Margulies, S. S., Thibault, L. E. and Gennarelli, T. A., 199. Physical model simulations of brain injury in the primate. J Biomech 23(8): 823-36. Meyers, M. and Chawla, K., 1984. Mechanical Metallurgy. Prentice-Hall, Inc. 182 IRCOBI Conference - Maastricht (The Netherlands) - September 27

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