Mathematical Modeling of Diffuse Brain Injury: Correlations of Foci and Severity of Brain Strain with Clinical Symptoms and Pathology

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1 Mathematical Modeling of Diffuse Brain Injury: Correlations of Foci and Severity of Brain Strain with Clinical Symptoms and Pathology Liying Zhang 1, Thomas A. Gennarelli 2 Abstract To address the relationships of clinical symptoms and pathology and the location and magnitude of brain strains, the Wayne State University human head finite element model was used with loading conditions posited to produce severe concussion (AIS 3) and mild, moderate and severe diffuse axonal injury (DAI) (AIS 4 AIS 5). Sinusoidal accelerations with peak thresholds of 8,1, 11,, 14, and 16, rad/s 2, respectively, were applied in sagittal, coronal and oblique planes to evaluate the effect of loading directions on brain strain distribution. Large maximum principal strains were consistently found in the thalamus, midbrain, corpus callosum and hippocampus. These areas seem to correlate well with observed clinical symptoms of memory dysfunction and altered awareness associated with concussion. Together with our previous study,.35 brain strain appeared to be a tissue injury tolerance for concussive injuries (severities of AIS 1 3), with the brain volume involvement of 5%, 2%, and 35% to be the thresholds for mild, classic and severe cerebral concussion, respectively..5 brain strain would result in more widespread axonal pathology, with 1%, 2% and 3% volumetric involvement being the thresholds, respectively, for mild, moderate and severe DAI. These proposed regional strain estimates can be used to allow the assessment of risk and outcome for the whole spectrum of diffuse brain injury. Keywords Head Acceleration, Brain, Diffuse Brain Injury, Concussion, Diffuse Axonal Injury, Finite Element Head Model, Brain Strain. I. INTRODUCTION Traumatic Brain Injury (TBI) is the leading cause of mortality and disability in the population < 45 years of age. Diffuse traumatic axonal injury (DAI) is a common pathology resulting from brain trauma and is believed to play a major role in neurological outcome [1] [3]. The underlying pathology of DAI is widespread damage to axons in the white matter of the brain and the level of immediate neurologic impairment is correlated with the extent and severity of axonal changes [4] [5]. The details of brain deformation in human TBI remain largely unknown, although they have been the subject of intense interest for the last two decades. Understanding the anatomical features of the neuropathology and severity of the lesion in relation to local tissue strain/deformation, the initiating event of the injury process, may lead to the development of injury thresholds to mitigate and prevent brain injury. Current US regulations use the Head Injury Criterion (HIC) to assess head/brain injury severity. However, the HIC only takes translational acceleration into account, not rotational acceleration, and TBI is attributed to both types of motion. Several rotational acceleration limits for diffuse brain injury have been proposed based on animal, cadaver, human, physical and human computer model studies [6] [12]. Recently [13] [14] reanalyzed previously published thresholds suggested for components of diffuse brain injury (DBI) to establish tolerances for the entire spectrum of DBI. Diffuse brain injury forms a broad spectrum of injuries from mild concussion, which is not associated with loss of consciousness, to classical cerebral concussion with transient disturbance of consciousness, to diffuse axonal injury with long lasting coma and sometimes resulting in a severely impaired outcome or vegetative state. Coma is characterized as complete failure of the arousal system with no spontaneous eye opening and inability to be awakened by application of vigorous sensory stimulation. Vegetative state refers to the complete absence Liying Zhang is Associate Professor in the Department of Biomedical Engineering at Wayne State University in Detroit, MI, USA (Mobile: , e mail: lzhang@wayne.edu). Thomas A. Gennarelli, is Emeritus Professor of Neurosurgery at the Medical College of Wisconsin in Milwaukee, WI, USA (tgenn@mcw.edu)

2 of behavioral evidence for self or environmental awareness [15] [16]. A number of computational models of the human brain have been used to further the understanding of injury mechanisms and to develop tissue level correlates for traumatic brain injury [17] [21]. Most recently, a validated finite element (FE) model of the human head has been successfully applied to relate defined head rotational parameters to localized brain strain patterns for two mildest grades of the whole spectrum of diffuse brain injury, mild concussion and classical concussion [22]. We postulated that these injury parameters affecting physiological function could also cause structural compromise in a continuum manner and the outcomes would be associated with the location and extent of affected regions. The current study, as a continuation of previous work, was conducted to relate proposed rotational parameters to localized strain measures for mild to severe diffuse brain injuries using this validated finite element model of the human head, the Wayne State University Head Injury Model (WSUHIM). Our hypothesis is that the differences found in the anatomical areas and magnitudes of brain strains for various diffuse brain injury severities would correspond to clinical symptoms and pathology common in humans with those conditions. II. METHODS The Wayne State Head Injury Model (WSUHIM) [21] was used to investigate the tissue strain responses at various anatomical regions resulting from a set of applied rotational threshold loadings (Figure 1). This high resolution finite element model features fine anatomical details including the scalp, the skull with an outer table, diploë, and inner table, dura, falx cerebri, tentorium, pia, sagittal sinus, transverse sinus, cerebral spinal fluid (CSF), hemispheres of the cerebrum with distinct white and gray matter, cerebellum, brainstem, lateral ventricles, third ventricles and bridging veins. The facial model consists of facial bones, nasal cartilage, temporal mandibular joint, ligaments, soft tissue and skin. The entire head model is made up of over 33, elements and uses 15 different material properties for various tissues of the head. Table 1 lists the material properties defined for the intracranial tissues. The model has been subjected to rigorous validation against available cadaveric intracranial and ventricular pressure data, relative displacement data between the brain and the skull, and facial impact data [21] [2]. The accelerations used as input to the WSUHIM were based on the rotational acceleration thresholds proposed for a spectrum of diffuse brain injury [13]. As shown in Table 2 and Figure 2, DBI is divided into six injury categories, namely mild cerebral concussion (MCC), classical cerebral concussion (ccc), severe cerebral concussion (scc), mild diffuse axonal injury (mdai), moderate diffuse axonal injury (MDAI) and severe diffuse axonal injury (sdai) [14] [23]. Previously, we reported the results of a study on brain strain responses to two rotational acceleration/velocity thresholds (4,5 rad/s 2 at 5 rad/s and 3, rad/s 2 at 25 rad/s) and correlation of the localized brain strain with clinical symptoms for classical concussion (AIS 2) and mild concussion (AIS 1) [22]. In the current study, the remaining four rotational acceleration/velocity thresholds (8, rad/s 2 at 75 rad/s, 12, rad/s 2 at 1 rad/s, 14,5 rad/s 2 at 125 rad/s and 16,5 rad/s 2 at 15 rad/s) which were posited to cause more severe diffuse brain injury including scc (AIS 3), mild (AIS 4) and moderate/severe DAI (AIS 5) were simulated using the WSUHIM. Similar to that used in the previous simulations, a standard sinusoidal function α(t) was used to construct the generic acceleration time histories with the peak values close to the above proposed magnitudes [22]. The time pulse duration (T) was varied slightly from ms in order to produce the best match for both peak rotational accelerations and velocities. The sinusoidal function for α(t) is as following: where A is the peak acceleration amplitude and T is the pulse duration. Figure 3 shows the rotational acceleration, rotational velocity and angular rotation time histories. The four rotational acceleration pulses were applied to the center of gravity of the head model in the sagittal (about y axis), coronal (about x axis) and oblique planes (about 45 xyz axis)

3 The affected brain regions were evaluated based on tissue strain damage criteria to assess the occurrence and severities of severe concussion and mild to severe DAI. In 28, Reference [22] reported the localized strain in relation to the occurrence and foci of mild and classical cerebral concussion. In that study, first principal strain of.35 was utilized which was based on the correlation of the head model prediction with over 5 concussive injury sustained by American football players [24] [25] [2]. In the current study, for severe cerebral concussion,.35 strain was used. For mild to severe DAI, a threshold strain of.5 was used to assess the injurious process involving structural damage to the cellular components and brain tissue. This strain damage level was selected based on the FE correlations of moderate and severe DAI sustained by occupants in real world accidents [26] [27]. The affected regions and associated brain volume fractions (ABVF) exceeding the strain threshold of.5 were also calculated and were applied together with the strain threshold to discern the severity/extent of diffuse axonal injury. The effects of the loading directions (about x, y, and xyz axis) on the distribution and magnitude of strains were compared to assess the heterogeneity of brain responses to a given loading severity. Fig. 1. Anatomically detailed finite element model of human head. TABLE 1 MATERIAL PROPERTIES DEFINED FOR INTRACRANIAL TISSUES Bulk modulus Shear modulus (kpa) Decay constant (GPa) Short /long term (s 1 ) Gray matter /2 1 White matter /3 1 Brainstem /2 1 CSF/Ventricles /.1 5 Poisson's ratio Elastic modulus (MPa) Dura mater Arachnoid mater Pia mater.45 3 TABLE 2 DBI CATEGORIES, DEFINITION, AND CLINICAL FEATURES Abbreviation Adjective AIS Concussion Grade LOC MCC Mild cerebral concussion ccc Classical cerebral concussion 2 4 <1 hr scc Severe cerebral concussion hr mdai Mild DAI hr MDAI Moderate DAI 5 5 > 24 hr sdai Severe DAI 5 5 > 24 hr Fig. 2. Angular tolerances for the entire spectrum of diffuse brain injury (listed in table 1)

4 Rotational Acceleration (rad/s 2 ) Rotational Acceleration (rad/s 2 ) Severe Concussion, AIS 3, LOC 1-6 hrs alpha(t) omega(t) theta(t) Time (ms) Moderate DAI, AIS 5, LOC >24 hrs alpha(t) omega(t) theta(t) Time (ms) 5-15 Roattaional Velocity (rad/s), Rotation (Degree) Roattaional Velocity (rad/s), Rotation (Degree) Rotational Acceleration (rad/s 2 ) Rotational Acceleration (rad/s 2 ) Mild DAI, AIS 4, LOC 6-24 hrs alpha(t) omega(t) theta(t) Time (ms) Severe DAI, AIS 5, LOC >24 hrs alpha(t) omega(t) theta(t) Time (ms) Fig. 3. The rotational acceleration and rotational velocity along with angular displacement time histories were applied at the center of the gravity of the head model to simulate diffuse brain injuries encompassing severe concussion to mild/moderate/severe axonal injury Roattaional Velocity (rad/s), Rotation (Degree) Roattaional Velocity (rad/s), Rotation (Degree) Temporal Response of Brain Strain III. RESULTS In terms of temporal progression of the strain response for a given loading condition, it was observed that the strain magnitude increased as rotational acceleration/velocity increased in all cases (with about the same time duration). The strain magnitude peaked at about 13 ms after rotational acceleration reached peak and at about 7 ms after the rotational velocity reached peak. Upon loading, the strain originated at the surface of the brain (cortex) first as a result of transmitted kinetics from the skull. Afterward, the strain deformation gradually propagated and migrated to the subcortical white matter and midbrain as the rotation velocity approached its peak. Eventually, at about ms, the strain peaked and accumulated in specific loci of the brain including subcortical white matter, deep gray matter and brainstem regions as listed in Table 3. Spatial response of brain strain The distribution of brain strain exhibited regionally specific patterns for a given loading condition. Figure 4 illustrates the brain strain maps on two representative coronal and horizontal sections due to applied severe concussive rotational acceleration in the coronal, sagittal and oblique loading planes, respectively. Using a critical strain threshold of.35 in the coronal rotation loading condition, high strain was found in the corpus callosum, midbrain, anterior commissure and external capsule. High strain also occurred in the subcortical gray matter including the thalamus, caudate nucleus, hippocampus and amygdala. For the sagittal rotational case, high strain affected various regions, mainly the cortical gray matter. These structures/regions were superior frontal cortex, cingular cortex, hippocampus, cingulum, brainstem and inferior fronto occipital tract. For the oblique rotational case, the high strain was concentrated in the septum pellucidum, midbrain, corpus callosum, thalamus, caudate nuclei and temporal cortex

5 Coronal Section Transverse Section Coronal plane rotation (x axis) Sagittal plane rotation (y axis) Oblique rotation (45 xyz axis) scc Fig. 4. Maps of the principal strain response on two representative coronal and transverse sections predicted by the head model as a result of head rotation applied in x, y and xyz 45 oblique axis planes at threshold level for severe cerebral concussion. Figure 5 shows the brain strain maps in two representative coronal and horizontal sections as the results of applied loadings associated with mild, moderate and severe diffuse axonal injury. At each given injury level, the effects of the rotational plane on the strain distribution and severity in the brain were compared as well. In the coronal rotation condition, high strain was localized in various regions in both white and gray matter. Particularly the high strains were found in the corpus callosum, cingulum, midbrain and temporal cortex. The high strains extended further to the thalamus, caudate nucleus, hippocampus and internal capsule in more severe rotational loading cases. For the sagittal rotational cases, the high strains were located mainly in the midbrain, dorsal pons, parasagittal white/gray matter junction, caudate and fronto parietal cortex. In the case of oblique loadings, the high strains were in the midbrain, hippocampus and fronto temporal cortex. The strain extended to the corpus callosum, thalamus, peri ventricular, internal capsule for MDAI and extended further to the cerebral peduncle, amygdala, head of caudate nucleus, basal ganglion and insula. Table 3 summarizes the affected foci of the brain tissue for strain >.5 as a result of loadings causing mild to severe axonal injury. Coronal plane rotation (x axis) Sagittal plane rotation (y axis) Oblique rotation (45 xyz axis) mdai MDAI sdai Fig. 5. Maps of the principal strain response on two representative coronal and transverse sections predicted by the head model as a result of head rotation applied in x, y and 45 oblique xyz axis planes at threshold level for mild, moderate and severe DAI

6 TABLE 3 Summary of involvement of various anatomical loci that sustained threshold strain of.5 or greater in response to the loadings proposed to cause diffuse axonal injury of various severities Mild DAI Moderate DAI Severe DAI coronal sagittal oblique coronal sagittal oblique coronal sagittal oblique WHITE MATTER pons midbrain cerebral peduncle internal capsule fornix septum pelludium optic radiation/tract corpus callosum cingulum GRAY MATTER caudate (head/tail) hippocampus amygdala hypothalamus thalamus basal ganglia insula cortex cingular cortex prefrontal cortex temporal cortex pareital : strain >.5; ++: if strained volume for the same region is greater than +. The affected brain volumetric fraction (ABVF at.5 strain) was calculated for mild to severe DAI loading conditions. For mdai, ABVF were 12%, 12% and 13%, respectively, as a result of coronal, sagittal and oblique head rotation. As loading magnitude increased to MDAI, ABVF reached up to 21%, 23% and 24%, respectively, for the corresponding loading planes. For sdai, ABVF were up to 33%, 36% and 37%, respectively. The overall affected percentage volume of white matter was relatively greater from oblique and coronal loadings than from sagittal motion. IV. DISCUSSION AND CONCLUSIONS The biomechanical mechanisms for the entire spectrum of traumatic brain injury need to be well understood in order to develop effective strategies to mitigate or prevent injury from occurring in the first place. The current investigation was conducted toward establishing the injury threshold correlates between the local mechanical parameters and loci of axonal pathology. The WSU head injury model applied in this study was constructed with over 33, elements with over 15 different tissue materials. The level of detail incorporated enables the model to predict tissue level response in various brain regions and tissues. Previously, the brain strain results associated with mild and classical concussion were correlated with anatomical regions [22]. The current study was conducted to relate localized brain strain patterns to defined head rotational parameters for more severe forms of diffuse brain injuries, i.e. severe cerebral concussion and mild to severe diffuse axonal injury according to proposed thresholds for a spectrum of diffuse brain injury presented in AIS 25 [23]. Model predictions indicated that certain regions of the brain were more susceptible to higher strains than others in responding to an applied rotational motion. We surmise the differing strain patterns to be caused by the heterogeneity of the material properties in various brain structures and tissues. Additionally, due to the non uniformity of the brain structures, the loading direction further dictated tissue deformation patterns leading to directionally dependent strain maps [28] [29] [21]. Similar to the directional effect on the strain distribution in concussive injury analyzed previously [22], the manner in which the strain related to neural dysfunction can be influenced by the presence of the dura partition (tentorium and falx cerebral) in the brain

7 The presence of the tentorium opening and its transverse orientation can affect the tissue deformation resulting from sagittal and coronal rotation. The excessive tissue deformation may therefore cause shifting and crowding in the region connecting the left and right hemispheres such as in the corpus callosum and upper brainstem regions. The falx may add constraint to the lateral movement in the medial surface of the parietal and temporal lobes, therefore facilitating the strain concentration in the cingulated gyri and limbic system (hippocampus, parahippocampal gyri, cingulate). The effect of the falx in sagittal motion was that the callosal region and thalamus were deformed because the independently mobile cerebral hemispheres were connected by the less mobile corpus callosum. In the case of oblique rotation, the strain field was more complex than that produced by a single loading plane with significant involvement of the midbrain and cerebral peduncle. In future study, brain responses to other effective 3D multiplanar motion will be investigated to fully understand the distribution of brain strain in relation to the neuro pathological consequence following a TBI event. The applied rotational acceleration of various severities induced multi focal strain in various regions crossing white and gray matter. The high strain was found consistently in the midbrain/ brainstem, corpus callosum, thalamus, hippocampus, cingulum and to some extent in the cortex in most cases. These regions conformed to the histopathological and neuroimaging findings in diffuse axonal injury after closed head trauma [28] [4] [1] [3] [31]. The cingulum is a band of association tracts that links the caudal and rostral cingulate gyrus with the hippocampus and parahippocampal gyrus critical for memory, manipulating information, spatial navigation, motivation and drive [32] [34]. The thalamus is known to play a key role in arousal regulation and support of consciousness. Postmortem neuropathological studies of TBI revealed that thalamic damage occurred in about 7% of the cases with DAI of grades II or III [35] [38]. The retrograde thalamic degeneration could occur as a result of widespread axonal damage. It could also be attributable to local tissue strain resulting from the mechanical loading at the moment of injury. The model predicted critical strain accumulated in the thalamic regions for all severities, suggestive of impairment of loss of consciousness in these cases. The midbrain and the tegmentum of the brainstem contain the reticular formation, medial lemniscus and spinothalamic tracts. These structures and pathways are of crucial importance for maintaining the state of consciousness and influencing cardiovascular function. The brain function could be directly impaired by injury to that region (primary axotomy) or may disrupt the neural pathways that communicate between multiple brain structures. Particularly, the reticular core in the brainstem distributes widely the axons that influence distant parts of the brain. The strain damage to this region could have widespread effect on neurological function. Our model predicted higher strains in these regions than in other parts of the brain, suggesting that disorder of the brain function in these regions is highly related to the tissue distortion in these areas. Along with results from previous studies on concussive injury [24] [22], localized brain strain appeared to have a direct mechanical relationship between the traumatic insult and the resulting diffuse brain injury. Traumatic diffuse brain injuries range from physiological disruption of brain function to severe structural compromise [1]. It is believed that concussive injuries involve physiological function while as the diffuse axonal injuries cause structural damage to the neural tissue/cellular cytoskeletal components, and include neurofilament compaction and impaired axonal transport. If the level of the strain could mediate the axonal integrity, then two strain thresholds would be necessary to differentiate the functional injury from the structural injury. In the current study the.35 and.5 strain levels were used to assess concussive injury and axonal pathology, respectively, while as the severity of a given injury type was assumed to be related to the extent and location of affected brain volume above a given strain threshold. Along with the previous study, the correlations of brain strain with anatomic regions associated with symptoms and pathological changes suggested that localized brain strain is a relevant injury predictor for estimating the DBI risk of various severities and outcomes. Together with our previous study,.35 brain strain appears to be the threshold tolerance for concussive injuries (severities of AIS 1 3), with the brain volume involvements of 5%, 2%, and 35% (>.35 strain) being the measures for mild, classic and severe cerebral concussion, respectively..5 brain strain would result in axonal pathology with 1%, 2% and above 3% volumetric involvement being the severity measures for mild DAI, moderate DAI and severe DAI respectively. For severe DAI, the upper rostral brainstem (midbrain, cerebral peduncle), corpus callosum and hippocampal gyri were typically strained to a great extent. It should be pointed out that the strain thresholds proposed for concussion and diffuse axonal injuries were model specific criteria which were dependent of the mesh resolution, material properties and boundary conditions defined in the model

8 In the current study, the strain thresholds used to predict the physiologic symptoms and axonal pathology in concussion and diffuse axonal injuries, respectively, were assumed to be the same across various tissues. It should be noted that using an in vitro model, Reference [41] reported region specific tolerance in the hippocampus and the cortex in response to the same mechanical stimuli. Due to mesh resolution (2 mm element size) employed in the current head model, the subregional heterogeneity of the material properties within the tissue could not be defined explicitly. As a result, the proposed strain thresholds from current model analysis may over or under estimate the physio pathologic outcome of diffuse brain injury caused by mechanical insult. The tissue level strain criteria proposed for the whole spectrum of diffuse brain injury from the current study were compared to those obtained from in vitro models. From the literature, according to the data from cultured axons of a dynamic stretch injury model,.77 strain did not sever all axons and primary axotomy occurred only at strain >.65 [39]. The reported strain thresholds (functional and cell death) using in vitro or in vivo models of TBI generally fell between.1 and.5 [4] [41]. Recently, reference [42] revealed that the strain level experienced by each axonal element was only one third of the total strain experienced by the brain tissue. Altogether, the current results were believed to be in line with the threshold data obtained from various TBI models. This paper completes the mathematical biomechanical simulations of the entire spectrum of diffuse brain injury for the first time. Future study will incorporate the anisotropic material properties for major white matter tracts such as the corpus callosum, internal capsule, spinothalamic and pyramidal tracts of the brainstem to improve the accuracy of the model predictions in responses to a multiplanar 3D loading event. V. REFERENCES [1] Gennarelli TA, Cerebral concussion and diffuse brain injury, In: Head Injury, , Cooper PR, Williams and Wilkins, Baltimore, [2] Christman CW, Grady MS, Walker SA, Holloway KL, Povlishock JT, Ultrastructural studies of diffuse axonal injury in human, J Neurotrauma, 11, , [3] Blumbergs PC, Scott G, Manavis J, Wainwright H, Simpson DA, McLean AJ, Staining of amyloid precursor protein to study axonal damage in mild head injury, Lancet, 344, , [4] Adams JH, Graham DI, Murray LS, Scott G, Diffuse axonal injury due to nonmissile head injury in humans: An analysis of 45 cases, Annals of Neurology, 12, , [5] Gennarelli TA, Thibault LE, Adams JH, Graham DI, Thompson CJ, Marcincin RP, Diffuse axonal injury and traumatic coma in the primate, Annals of Neurology, 12, , [6] Ommaya AK, Yarnell P, Hirsch AE, Harris EH, Scaling of experimental data on cerebral concussion in subhuman primates to concussion threshold for man, 11th Stapp Car Crash Conference, SAE 6796, [7] Ommaya AK, Gennarelli TA, Cerebral concussion and traumatic unconsciousness: correlation of experimental and clinical observations of blunt head injuries, Brain, 97, , [8] Lowenhielm P, Mathematical simulation of gliding contusions, J Biomechanics, 81, , [9] Löwenhielm P, Tolerance level for bridging vein disruption calculated with a mathematical model, J Bioeng, 2, 51 57, [1] Margulies SS, Thibault LE, A proposed tolerance criterion for diffuse axonal injury in man, J Biomech, 25, , [11] Newman J, Shewchenko N, Welbourne E, A proposed new biomechanical head injury assessment functionthe maximum power index, Stapp Car Crash Journal, 44, , 2. [12] Zhang L, Yang KH, King AI, A proposed injury threshold for mild traumatic brain injury, J Biomechanical Engineering, 126(2), , 24. [13] Gennarelli, TA, Pintar FA, Yoganandan N, Biomechanical tolerances for diffuse brain injury and a hypothesis for genotypic variability in response to trauma, Proceedings of Assoc Adv Automotive Med, 47, Lisbon, Portugal, , 23. [14] Ommaya AK, Goldsmith W, Thibault L, Biomechanics and neuropathology of adult and paediatric head injury, British J Neurosurgery, 16(3), , 22. [15] Plum F, Posner JB, The diagnosis of stupor and coma, 3rd ed. Philadelphia: FA Davis, 198. [16] Bernat JL, Question remaining about the minimally conscious state, Neurology, 58, ,

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